seriously? Bag the bikes. We went to a shop downtown, right off the main square and negotiated a 16 dollar a day rate for a scooter including gas and everything.
It was a BLAST. We had a ball zipping around on that scooter and we pretty much covered the island. We went from the lighthouse clear down to El Cedral and back, we went from our hotel (mi casa en cozumel) to the dive shop (DWM) and back with all our gear (gear in a bag on the foot rest between my knees) and with me and the wife on it no problem.
I was worried about it cause I'm huge (6'5" and about 330 lbs) and my wife is very tall 5'11" and I thought it would struggle. it did 60kph easily and was easy to drive.
They are also very easy to park anywhere. A bike would be fun but nowhere Near the utility a scooter gave us. I'd look into that. Ours was about 100 for the entire time we were there. You couldn't buy or ship a bike for less than that and I think you'd lose the bike between every trip, or the tires would be flat or something.
honestly, we had as much or more fun zipping around the island on the scooter as we did diving. And I think we saw pretty much every place on the island, or close to it.
And you're among the very few that didn't come home with road rash or worse.
Do a search for moped rentals here, and you'll probably learn alot and probably think twice before you do it again.
UCRTWF = PLEEASE DO NOT RENT A SCOOTER....THIS IS HORRIBLE ADVICE!!!!! Especially as the island gets busier for high season.