"Are there places you can enter the water and dive from shore ? Also, do the dive shops only cater to those staying at resorts or cruise ships? We will be staying in first bight and seemingly the dive operators around do not take people from off premises, is this true? Any information you can provide would be great, thank you."
There are many excellent shops will take anyone not staying with them or from outside it matters not.
In short you won't find many spots (dive sites) that can offer you this though I do know of some places you could have a reasonable shore dive, you might have a few problems getting some fills and you would need to register with the marine park in roatan. Coco view and Fantasy Island offer shore dives if you are staying with them.
The biggest problem is that the reef while close is mostly too far to swim out, At seagrapes point and cocolobo resort you can get pretty close to some dive spots off the top of my head seagrapes escape, divemasters choice and the famous deep dive of hole in the wall might be possible.
Safety would be a problem with a lengthy surface swim.