Using 34mm square timber, I constructed a simple frame using butt joints strengthened with dowels. I'd never tried this before, so I'll be interested to see how the stand up to regular use in a student house.
There's not much to say about the construction. The two sides are made up first and joined with the three rails to create the frame. It's not just an aesthetic thing to have the bottom open. It makes getting the bag out a little easier. I've also considered making one with a crate on runners for bottles or cartons at the bottom. Version three perhaps!
The top is just another rectangular frame made like all the others. The case clips are on both the front and the back, allowing the bag to be put into the frame and then clamped in position with the top frame. You could just as easily hinge the back. I added some soft closure bumps for cabinet doors to give the frame more grip on the plastic bag.
So far the reports have been good, it's working fine. Another successful piece of utility woodwork!