The pot depth is generally determined by the circumference of the bonsai's trunk just above the soil line. If the circumference measures 3" then a 3" deep pot is used. The vast majority of bonsai pots are shallow, wide and oblong. HERE is an article on the subject.

One thing is where are you with the bonsai? If me and it's a little thing and I want it bigger, then I'll put it in a larger pot, doesn't even have to be a bonsai pot. Ideally it should go into the ground, but lacking space for that, a big pot works. Let it grow and get bigger in the pot. Leave any twigs and branches that are lower down on the trunk. This helps thicken the base of the tree. Then when you ready you can look for a bonsai pot that works and transfer it into that.

If the tree is the size you like, and you like the pot it's in, then I would, at the proper time, pull it out of it's container. Rake and trim the roots and replant it in the pot it's already in. Easy. ;) HTH