There are no good studies that look at exercising after filler injections but I usually advise people to minimize activities that will significantly raise their blood pressure as that can contribute to swelling. Juvederm absorbs water during the first 48 hours and so often there is an "over-correction" or very full appearance to the lips at first which is normal and goes away. It is unlikely to significantly alter your final result but I'd discuss that with your injector. What I do warn patients about is not to manipulate the area for the first 48 hours with intense kissing, massage, etc so as not to misdirect the filler and have them use ice compresses while in the office for 10 minutes immediately after injection. If you do plan to take the trip, you can ask your doctor about a low dose of oral Prednisone after treatment because that might help a bit with swelling that you may get.I hope that helps!
If you are going on a bike ride like you are describing, it is probably best to wait until after the biking to make sure you maximize the results from the procedure. You can always find someone willing to do the injections, but these products can swell, and with exertion this swelling can get even worse. Wait; you will be much happier in the end.