I am flying first time my road bike across country for a bike race.
first time using a bike box, which would be the hard case
for those who have used them
is there room for a floor pump in to the bike box?
can i fit my helmet? thanks

Depends on the particular bike and box. I wouldn't carry my helmet in a box, I'd carry it with me out of fear of damage. Pump, I'd pack a frame pump capable of getting your tires where they need to be, that should easily fit in the box, like a Topeak Road Morph G.

I am wondering what the reason is that you can't experiment for yourself. Have you actually tried to put your bike in the bike "box" which really is a case from what you say? And then have you tried packing the other stuff around the bike?

FWIW, a bike box is not a bike case. I am about to pack our bikes into bike BOXES which have already done three or four international trips... and yes, I can fit a floor pump and helmet in one of them with the bike. I have never used a bike case which I regard as a large capital investment for something that a $15 properly sized and constructed cardboard box can do (or a suitcase if you are carrying a Bike Friday or some other folding bike).

I do, however, take the trouble to wrap each bike and the front wheel and the handlebars in cling-wrap/saran wrap, which has the triple advantages of (a) keeping the parts together; (b) protecting the finish on the frames and parts and (c) enabling inquisitive security personnel to lift the whole lot out and put it back in the box without losing parts or cramming it all together with the risk of damage.

Also as a by-the-by, because we are renting an SUV on our impending trip to Canada, I also will be packing in one of the bike boxes a bar carrier for both bikes so the bikes, with front wheel removed, can remain upright in the back of the vehicle, rather than risk damage lying on top of each other.

In the end, it comes down to weight limits and what the airline will allow you to carry before imposing penalty surcharges or directing you to freight your bike to your destination rather than carry it on the same flight you are travelling.

Bike boxes come in sizes. Since you are packing a road bike, you are going to want a larger size box. If you are scrounging a bike box from the bike shop, ask to look inside at a factory packed bike. EVERY LITTLE DETAIL COUNTS so don't skimp on anything.

Here's a hint. Remove the front wheel and package up the bike outside of the box. Then stand the box up on one end and set the bike into the box on it's rear wheel.