I thought European vendors use international post or DHL.
At the very least, verify with Bike24.com that this was fed ex. Better yet, get the tracking number from them. If Fed Ex is legitimately billing you, the tracking numbers should match.
Scammers rely on coincidences, so that 1 in 10,000 attempts works. The fact that the bill came by mail, however, suggests it might be legitimate (email is free, snail mail is not, so less cost-effective for shotgun-approach scamming).