An even newer update to Whithers' original helpful post and danw's update that I hope helps those new to Houdini (hopefully Whithers won't mind my copy/paste of much of his original text). I added a few more steps since I'm being very explicit:
The vertex node you want in Houdini, at least as of v. 17.5 is called "Vertex - Old." The new node called "Vertex" is an Attribute Expression sop and doesn't work with these specific instructions.
1) Plug the File node with the bgeo sequence into the desired UV sop ("UV Project", "UV Texture", etc).
2) Plug that UV sop into a "Time Shift" sop.
3) Click in the "Frame" field of the "Time Shift" sop and change it to 1 (or whichever frame you are "locking").
4) Connect the "Time Shift" sop to the second input of the "Vertex" sop. Again, it's actually the "Vertex - Old" sop.
5) Connect your File node (your imported .bgeo file) into the first input of the "Vertex" sop.
6) Click on the "Vertex" sop and about halfway down, change the "Keep Texture" tab to "Add Texture."
7) You will see green boxes that say @uv.x, @uv.y and @uv.z. Change these to @uv2.x, @uv2.y and @uv.2.z. The original instructions confused me at this step and I first changed it to @uv.x2, etc. which doesn't work
Your texture should now stick to your geometry. I even applied it to a specific piece of my entire .bgeo animation (using the blast node to separate it from the rest) and it worked great. Thanks again to the previous posters for their instructions. Hope this helps on the newer versions as well.