I don't believe that there would be any restriction on carrying a bike.
If you can manage to carry 18 days worth of stuff, a flight bag, a laptop and a bike you're a better man than me. Don't forget the jumpseat or commercial flight to/from your starting point, or the mid line commercial repositions. Plus, most of the typical hotel transports seem to get full with just normal crew baggage.
Besides, most guys won't help you carry your stuff unless you're a cute F/A!
