Most people will recommend that you tear away the peat pot from the plant before transplanting to the garden. I very heartily agree with that opinion,it takes a lot of time for the roots to grow through the pot. What I do is to dig the hole just a little bit deeper and crumble the peat pot up and put it in the bottom of the hole. But in answer to your original question you are supposed to bury the peat pot completely.

I've used peat pots extensively for beans, with great results. You can encourage root growth through the pots by pushing the pots into a tray lined with play sand after planting. The roots will grow through the pots into the moist sand. If removed carefully during transplanting & kept moist, these extra roots result in little to no transplant shock.

I do not recommend removal of the peat pot before planting, since this will cause root damage. If you intend to remove the plant, then you should use a container from which the root ball can be removed intact, such as plastic cells.

However, if you use peat pots, then you can - and should - tear off the top edges before planting. It is important that no part of the peat pot be exposed above the soil line. This would wick moisture away from the seedling, delay root growth, and can even result in the garden soil pulling back from the pot.

I generally pack my soil-less starting mix to the top of the pot, so there is very little rim exposed. Beans should not be transplanted much below the original soil line. I tear away any protruding edges, then bury the pot so that it is just barely covered, with about 1/2" of soil. To prevent rain from exposing the pot (and to keep it moist until the roots establish themselves) I apply a mulch of grass clippings around the base of the plants.

Oh, one last tip. To avoid excess pot being exposed, don't use bigger pots than you need. Most common beans do well if started in peat strips that are 32 to the tray. Smaller beans like adzuki, mung, and cowpeas can be started in strips that are 50/tray. Large limas and runner beans might require larger pots.