The bx22 and bx23 3 pt hitch is a unique animal. Since it had to be removable in order to put the backhoe on there are some pretty special pieces that go along with it. Most 3 pts are just a couple of lower arm with some kind of chain or turnbuckles to hold them in place and a top link. The bx22 and bx23 have other pieces besides those to make it work. On top of that, the bx22 and bx23 have what is known as a limited cat 1 3 pt. Meaning the over all geometry of it is smaller than a standard cat 1 hitch. The lower lift arms are shorter, the top link is shorter and the space between the lower lift arms and top link is also smaller. I would think to find an after market hitch for one of these tractors would be problematic.
Unlike the bx25, the 3 pt hitch was not an option on the 22 and 23. It was standard equipment. Is it possible to go back to the party you bought it from and ask him if he is sure he doesn't have it laying around somewhere? The other option would be to order one from a Kubota dealer and that is only if they can still get the parts. If you could find a parts manual for your 22 that will show you all the parts you would need to acquire. Here is a pic of my 23's 3 pt hitch. You can compare what you see in this picture to what you have and you should be able to see what all you need. Of course a parts manual would be the way to go.