Holding my bike front wheel up, and spinning the wheel, I can feel on the hand holding the bike some murmuring, it spins smooth though without any drag. I guess that this must be a sign that the bearings are coming to an end and most likely the rear wheel is the same case. Am I correct? It is a road bike with some 12K km on it, with sealed bearings. How long can I keep riding it before getting it serviced? My LBS man is away on a sick leave. Can I ride it for 100-200 Km more, or should I put the bike aside until he gets back?

Usually, 12k km is just at the breaking-in point as long as it's not getting crunchy or stops spinning freely. I always try just carefully removing the outer seal, no need to remove the bearing from the wheel, and giving it a good flush and add more grease. You can easily triple the life of your bearings by doing this rather than replacing.

I will try it, although I have never done anything like this before. For the rear wheel I feel safer letting the man at the LBS do it.

What is "murmuring" in relation to a wheel?

Noises aren't usually a good indicator of a issue for wheel bearings. IMO. Even for bicycles I had without sealed bearings and even no dust seal at all, they'd get a little bit of grit or sand in them and I'd hear some crunching noise for a little bit. However the bearings still lasted a very long time. I only remember replacing the bearings on those bikes during the few times I dropped a bearing and lost it.

Wheel bearings and races are pretty hard material. They'll pulverize most stuff that gets into them and not be any immediate concern. At worst you get a slight reduction in useful life. But not usually anytime soon.

My current bike has sealed cartridge bearings. And is over 12K Km (8000 miles) I won't think about replacing them until the axle and hub show a lot of movement radially (perpendicular) to each other. A small amount is normal, IMO. So don't fret about that. And only look at the movement between the axle and hub center. If you are gauging it by the movement of your rim or tire, then that is on a arm almost 311 mm (12.2 inches) away making a tiny bit look like a lot.

If you happen to ride in competitions a lot, then perhaps I might change my answer.

Not any racing, but what scares me most is ruining my wheels. I would like to service these myself, but I really have no idea. Funny, when I raise my front wheel, the valve being logically the heaviest part of it instead of turning the wheel so that it gets at the lowest, it turns nice and smoothly untill it stops always at 9 o' clock.

the heaviest part of the rim is the factory joining point, opposite of the valve.
tubes and tires are never totally balanced.
any slime inside the tube or tire throws off the balance too.

and, unless the bearings are extremely high quality, they will always produce a bit of noise, when amplified by the spokes and rims.
grease that totally eliminates noise is too thick, and will cause excessive drag.

What type of bike is yours? MTB? Road? Comfort?
what brand/model hubs?

There are different types of bearings that are called "sealed".
Old style cup & cone bearings can have a "seal".

Cartridge bearings are another type. More modern applications.
IF that type, you really aren't going to hurt them by riding until they definitely "tell you". they're bad.

The other type needs "normal maintenance". Damage can result to the cone & cup(hub)

What is the brand & model hub?
That may give us the info to Intelligently advise you.

Early 80’s WTB Greaseguard hubs on my mountain bike still going strong.

It is a road bike.
I am trying to grasp if it is time to replace the bearings on my bike. Is there a way to tell when that noise from the bearings is much enough to indicate the need of change of them? Considering they are cartridge bearings, is there a risk of damaging the wheels while using it till the man at my local LBS gets back?

Well said (you see how far my knowledge on this goes...). They are cartridge bearings on Axis wheels of a Specialized Alez Sport 2021 bike.
When do they "tell you" they 're bad? So far I feel something like a murmuring/vibration on the bars while holding the front wheel up and spinning it, but it runs smooth.

Unless you’ve left this out in the rain or ridden through 2’ floods, there’s no way these need replacing.

Always stored indoors, never in rain, but there are some 12K km on it.

I did 15k km last year. Haven’t replaced any wheel hub bearings in 10 years.

I imagine he's feeling a slight rumble.

Take the wheel out of the fork, fasten the quick release using appropriately sized spacers such as stacks of washers in place of the fork ends. Then you can feel just how rough the bearings are by turning the axle by hand. I wouldn't be surprised if the bearing adjustment is loose, in which case you"ll want to press the axle in as you turn it, on each side, to feel pitting or grit. Report back.

Take the wheel off the bike turn the axle in the wheel with a light touch. If you feel any grinding or binding, then you can clean and lube the bearings as described by removing the dust seal. If there is still binding after that, you might have gotten a crap set of bearings. No road wheel should be experiencing bad bearings after just over 7,000 miles.

The point I was making is that you aren't going to damage anything "worse", unlike ignoring a cup & cone type where ignoring those can result in destruction of the bearing parts that may be difficult to source & replace.
When the cartridge bearing gets rough enough that it's noticeable when riding, then replace. Unless you're going on an extended tour etc.

Take the wheels out and turn the axles by hand. If they feel notchy or dry, or if there's lateral play, then it's probably time. As said before, with cartridge bearings you won't damage your wheels by continuing to ride them.

Did tried the hubs with the wheel in my hands and it is smooth. I cannot do the same with the rear for which at least there is no lateral play. Today, just before going out for my Sunday ride, a fellow cyclist tightened the skewers even more. 100Km and the feel was quite different. The bike felt sturdier and that feel or murmuring was quite a lot less! I must put a bit more soul in opening the skewers, but it did wonders.

"Spins smoothly" and "murmuring" are contradictory info.
the momentum of the wheel's weight makes even nasty, rusty, over-tightened hub bearings "spin smoothly", in some folks' opinions.

unless the hubs are high end and feature expertly polished bearing surfaces (Excellent condition DA, some Ultegra, and The Highest echelon of a couple other brands), there will always be some "murmur" happening...

best way to assess bearing quality and adjustment is to remove the wheel, THEN turn the axle, while feeling for any roughness... many simply need a bit of play added to compensate for the "QR tightening" effect.
Zero play when the wheel is off the bike means Too Tight once that QR is closed on the frame...

old, hardened Grease causes roughness.... as will ANY tiny pits in the races.

Sounds like the rumble you can get from slightly loose bearings, gone away with proper QR pressure. The bearings could still be in need of servicing, and running them tight as they are now can cause rapid wear, but with luck that was just a "running in" phenomenon and it will now run smoothly.

I suppose that completely destroyed cartridge bearings could stop you in the middle of a ride. I've never seen this, though. I think they get obviously gritty and noisy, with obvious drag, way before that happens.

The rear hub has 2 bearings for the bike weight on the hub (in green here), and two or three bearings on the removable hub shell (in blue) where the cassette is mounted. This takes the pedaling force from the chain. These have smaller balls to fit within the hub shell.

For example, from https://singletrackworld.com/forum/b...-superstar-v6/

Is that called a hub shell? Not just a freehub?

That's the freehub body, the green part is the hub shell. I guess you could call the bare freehub body without its bearings pawls and springs a freehub shell, but that would be ambiguous because the whole hub might be referred to as a freehub vs freewheel hub - nobody says "freehub hub" do they??

Yeah he was talking about the blue/purple bit though