A friend and I stamp at each others' home every couple weeks. Here are some things that help cut down what we transport:
Know what the other person has and share those items.
Never transport ink pads unless it's something brand new that the other person doesn't have yet.
Agree to share common colors of cardstock. If you switch off houses regularly, it all evens out in the end.
I also keep a small tote like this
on my workdesk. It holds the things I always use - bone folder, adhesive, ruler, dimensionals, glue dots, etc... When I'm headed out I just grab it and go knowing that all my essentials are in there.