You could get a dog kennel--one with either chain link or large-size wire mesh.
Lots of kennels come apart into flat panels, so you can take it apart and move it as often as needed. I'm thinking of the ones that are 8 feet or 10 feet square, or you can add more panels to make them bigger yet. A single panel is awkwardly large, but I think most adults can manage to handle one panel alone. Just move it piece by piece, if you don't have a helper.
A "dog kennel" should be dog proof, and might even slow down a bear.
Use either wire mesh, or more of the same panels to make a top, then add a tarp to keep rain and sun out.
To keep things from reaching through the large mesh, put hardware cloth over the bottom part of each panel. If you put the hardware cloth on the inside and attach it with zip ties, I think that will be secure enough.
I don't know where you live, but I am assuming that it's summer right now, so a tarp on the roof and maybe a tarp on one side should be enough shelter for the next few months.
You can buy dog kennels from various stores, but you can also find them on craigslist sometimes. And they're just handy to have around for temporary and portable pens