Bermuda in May is warm (high 70s low 80s) but it's also usually pretty humid and the temperature doesn't drop significantly at night. It rains pretty infrequently in late spring and summer and usually only for an hour or two, so not a big deal to bring a rain jacket especially if you are at the beach or the pool
There's a few different ways to get around but gas powered cars are not available to rent for tourists, luckily Bermuda has a great bus system (and the rides are always a fun experience). You can rent gas powered mopeds as well as small electric cars (2 seats) right from the Grotto Bay Hotel . There are plenty of taxis available but this is probably not the most efficient way to get around if you're staying for more than a couple of days.
Funny you should ask such a specific question but interestingly enough there are plenty of great spots around the island! - Blue hole park has a short jump into a very protected blue lagoon and some small caves that you can swim into - Watford bridge is a decently high jump (~15') on the way to Woodys, Mangrove Bay, and the Cruiseport a great way to cool down. - Admiralty House Park has a few different heights to jump off of and has awesome views and is the best place to get some great photos jumping in. Once in the water you can climb (staircase) back up through the caves and do it all again!
there are a few different places on the island - find them here: https://www.pabermuda.com/where-to-play