I'd guess they use robotic surgeons all the time, but with human guidance. I think that's a lot of what happens under the cover of the bio bed.

Biobeds in Star Trek can perform simple surgeries by themselves (simple meaning still finer and more detailed than anything we can do today). On Star Trek they can create energy fields that feel as solid as matter. The biobeds can create such fields anywhere they want, meaning that any "simple", predefined surgery can be carried out automatically with extreme precision, often without breaking the skin.

Of course if it's a surgery that doesn't have exact, predefined instruction sets (which tends to be what happens when we the viewing audience are watching, for dramatic purposes), then it has to be carried out manually. Sometimes this is done by manually controlling the biobed (only seen a couple of times onscreen), but often the surgeons just use hand held tools with similar functionality, and just use the bed as an advanced fMRI to guide their decisions.