Often, bonsai are grown intially in the full ground. This is the fastest way to get a reasonable sized trunk. After that, once the tree trunk is ready, most of the scars have healed and the main branches are in place, the tree is lifted from the ground, and placed in a training dish. Normally a shallow pot, much larger than a bonsai tray. Over time, as thetree gets mre refined, the tree is moved into smaller pots.
Now.. CAN you keep a bonsai in a gardenbed? Yes you could. It will not be easy to keep it refined. It might not qualify for the label bonsai (Although garden bonsai do exist). But they may still be nice to look at.