Don't know about Vero -- it's been a while since I've been there.
You CAN rent bikes at HH, either through the resort, or from a private company that will deliver them to the resort. We've only done them through the resort, although many have said that you can get a better deal through someone else.
The HH resort itself does not have a bike trail, but there are LOTS of bike trails all over the island. You can pretty much get anywhere on a bike. A lot of people even take them down to the beach!