Bonaire or Grand Cayman are both fairly easy to get to and really safe. Probably the two best dive locations in the Caribbean also.
On Bonaire, just about everybody at the
diveresorts are divers so finding a buddy is no problem. And you can do boat dives and the resort's shore dives - most of them are just off named dive sites - without having to venture out on your own. I can just about guarantee that you'll be able to find a group to tag along with there, we were asked about 3or4 times. And Kralendijk is safer than my neighborhood at night.
I'm not sure they have any crime in Cayman either. Must be something to do with the 200 banks on the island...

. There are a bunch of smaller dive ops on Cayman that would be good to dive with even solo. They put a DM in the water with you and generally the group stays together. Neptunes, WalltoWall, Red Baron are all good choices. Most do 8-10 divers per trip also. It's typically deeper diving there though, at least for the 1st dive 80-100' is not unusual due to the clarity of the water, there's interesting stuff to see at that depth. Red Sail is another option, the groups will be larger but dives are shallower since they deal more with resort and cruise dives.
Downside of most liveaboards is that you'll share a room with a same sex single if possible. Or get your own by paying a single supplement - on Nekton it's 50% more.
We had 3 single women on our trip, one dove with us a couple days. After the first day on our trip, people were pairing up all sorts of ways - we did dives with 2, 3, 4, 8, 12(that didn't work so well) people at different times. And - at least on Nekton - if you can't find someone to pair up with, the DM's are glad to go with you if asked in advance. There was a couple who were new divers, they dove with their own DM a couple of times, I don't think it cost them anything extra either - you might want to confirm this though. Normally - at least on our trip, the DM"s did not dive.