Just thought I'd follow up. We didn't end up using the bikes quite as much as I envisioned (I was thinking we'd do long rides during the cool mornings of the non-dive days we spent in town, but we didn't get the bikes 'til we were at the Blue Angel and using our mornings for diving), which is to say there were no attempts to transverse the island. We did log about 25 miles out and back down toward Punta Sur one hot afternoon. And we did use the bikes as basic round-town transportation.
The cyclopista is really nice, if not fully devoid of cars. I enjoyed cruising by wetland areas and occasionally hearing something big go crashing into the water as we passed. I like to think they were crocodiles. I ride about 100 miles a week at home given decent weather, but it's mostly on a nice, light little road bike. Though the Scott bikes are of much better fundamental quality than most of what's on the island, the huge, knobby MTB tires were an adjustment I didn't love. I also started out with a really worn seat that was weirdly angled down in the back, which was hard on my back. Mr. Tomas at the Tuk Tuk was great about letting me swap it out. He doesn't speak much English, and my Spanish is limited, but it worked out. I believe Rogelio that he has the best-maintained rental bikes on the island. They weren't perfect--my husband had a slippy seat, the brakes were rough and I have no idea if the tires were properly inflated (some tires had Presta valves, making me think the smart money would be on bringing a gauge and pump). But the gears worked, the chains were good and nothing was bent. There was some rust. My bikes all have nicknames. I called this one "Beast."
The churro guy had recognized us riding around and warned us the first morning that Cozumel drivers have "no respect" for people on bikes. But it really didn't seem that bad (we ride on much more congested streets at home, with no lack of inattentive, easily irritated motorists), and in our limited wanderings, it seemed that people gave us the right-of-way when we were legally entitled to it. At night, we lashed dive lights to our handlebars. At home, I'm so paranoid about bike theft that I'm very selective about what bike I'll lock, and where, and with what (cheap u-lock and/or huge, heavy chain), so it was a nice change to feel we could go into a restaurant and lock up using the little cable locks that came with the bikes. At night, we dragged the bikes up the stairs and kept them in our room--yay for being only on the second floor.
Would I do it again? I'm not absolutely sure, under present circumstances. I loved the freedom. But We had a couple days where bikes sat idle. And there was grousing in some quarters the night it stormed. Maybe I'd keep them fewer days, in retrospect. I'd still love to ride the island's perimeter. But I may have to see if there's a reasonable way to get there with my own bike. Doesn't look like the legacy carriers are it, though.
Things to know about Sombrero: cash! Bring your own helmet, lights, emergency kits etc. if you want them. Locks provided. Bikes have water-bottle cages.