On the MUP I call out or hit the bell a good distance from any group. I like "bicycle coming though" - said slowly and clearly. I often get a "thank you." Out on the road I really appreciate it when passers say something friendly like "hi, how's it going?" So I usually say something before passing. I've been startled by people passing too close, and it does make me bristle momentarily.
I haven't seen many rabbits, but I stopped for a family of geese the other day. Out here the squirrels are crazy, literally, they panic at the site of a bike and zip back and forth several times before picking a direction. Well and the screaming cyclist probably doesn't help. We also get big groups of wild turkeys, and I'll stop for them. No telling what they'll do, and they're huge!
Speaking of turkeys. I was on a narrow, winding, no shoulder road and needed to pass a guy who was tooling along at a slow pace. This was not a road for riding two across. I announced that I needed to pass and proceeded to do so. I guess he took this as a social opening, and started up a chat - and sped up! He also started drifting into the road towards me. (I’m female, which was probably my first mistake. It was the "do you ride here often?" line. Yep.) So there I am stuck in the middle of the road with this idiot going on and on... Unreal. I finally told him sternly that I needed to finish passing. Fortunately we were headed into a climb and I dropped him. :-)