The consensus seems to be that if you book/check-in with BA then there's no problem (this isn't the policy as-written though as BA state they won't be held accountable if partner airlines add extra fees for your luggage).
You're not going to interact with any AA staff till you're on the plane and by then it seems a little late to ask for the bike fee?
I guess it's possible that BA could ask for the bike fee on behalf of AA, but that doesn't seem to be happening at the moment.
Don't forget to set up a BA executive club account, it's seriously worth it, even for one transatlantic flight, you earn almost enough points for a free return to Europe.
You can claim back points up to three months after you fly.
And once you have points, they never expire, as long as you earn a mile every year.
You can also get your tesco club card points added to it, also really worth it, £250 spent is like 600 miles.
Don't forget to set up a BA executive club account, it's seriously worth it, even for one transatlantic flight, you earn almost enough points for a free return to Europe.
You can claim back points up to three months after you fly.
And once you have points, they never expire, as long as you earn a mile every year.
You can also get your tesco club card points added to it, also really worth it, £250 spent is like 600 miles.