recommend taking amtrak with your bike on a little test run...maybe from the downtown san diego or old town san diego station after sunrise to solana beach or oceanside and riding back.
whether buying the ticket via the amtrak app or off their website, you will need to indicate that you are bringing a bike onboard (there is an option/screen for this). it is no additional charge.
ime with a bike (approx 20x) on that line between san diego and los angeles, the bicycle storage car is the northernmost (closest to la) car just behind the engine, regardless of whether that
line is heading north or south. the bicycle storage car has approx 5 seats squeezed in between the large bathroom and the bicycle storage area (think there is space for 6 bikes total-3 on each side
of the car). these seats are designated for those with disabilities. you can use them but if a disabled person arrives (and you're not disabled) and there's no more room in that area, you will
need to/be asked to move. dunno how much bigger your bike is than a mtb but have seen plenty of mtb's on there over the years. pretty sure if you've got panniers/extensive bike storage containers mounted
on the bike, you'll have to remove them and bring them with you to your seat. if you're taking the line from sd to la, it's usually pretty quiet on that first 4am weekday amtrak train until just after
6am when the train hits irvine. ridership picks up substantially after that through the santa ana, anaheim and (esp) fullerton (the last stop before dtown la-union station). heading south in the pm, it's just in reverse.
plenty of room once people get off in irvine.

normally, i only take the amtrak between sd and la on mon or tues. have only sat down by the bike area if that day is a federal holiday where there is much less commuter traffic. on a normal mon or tues,
detach my garmin computer, blinky lights, saddlebag and garmin varia radar, use my ottolock to attach the bike to the metal guide rail along the side of the train car wall and climb the stairs to sit on the
second level of the (same) car as the bikes. if you're wearing bike cleats, be careful on the stairs and use the handrail. food/drink car is usually in the middle car on the train if so inclined.

supposedly, amtrak will not be operating nonstop between sd and la during the week without the current disembarking of the train and bussing up to irvine, then reboarding the train to la (or the reverse heading to sd) until late march
or early april. this is due to the track repairs being done in san clemente. apparently sat or sun riding (when it's less crowded), the train is going to/from la without de/reboarding + bus between irvine and oceanside.
personally waiting till repairs are complete before doing a 2 or 3x a year la to sd ride via amtrak but it may prove handy for you to just do a previously mentioned "quickie" to the 1st or 2nd stop to better figure out logistics to avoid
potentially bigger issues/disappointment down the road. hope this helps. if you're credit card touring and staying at hotels/motels/etc for those 3-7 nights, makes a big difference in the amount of stuff (vs camping) that you're
lugging along in panniers. if you do indeed end up riding from solvang area or points north of san diego county back home, it'll likely be worth your time to get the yearly camp pendleton pass to avoid riding on the 5 freeway. worse case scenario,
you can either ride the freeway or catch the train in san juan capistrano and get off in oceanside (or all the way back in sd).

getting to solvang (without riding) involves a bus transfer from the santa barbara station. dunno how that works with bikes, esp a bigger one. amtrak has semi-nearby stations in oxnard, santa barbara (closest), san luis obispo and paso robles. getting off
at any of those stations and riding north or south (and potentially taking the train back some or all of the way back) would be a fun trip with support here and there along with a few decent grades and plenty of scenery. happy touring!