Do you need such a big trash bin? Do you have room for 2 smaller ones, for trash and recycle?

My wife just wants something you can fit those costco 13 gallon bags in...

Did you try Ikea?

Isn't 13 gal the standard kitchen bag size? That's what I use, and my trash can measures about 10 x 14 on top and 17" high. My garbage bin came with the pull out, and the pullout works like you say - there is a shallow base that holds the bin, as well as metal bars halfway up to keep the bin steady. I have empty space behind mine where I keep the garbage bags, among other things. I think it might be rev-a-shelf, that's what I think my cabmaker uses. But I don't think a 13 gal bag will go in anything much bigger, not 20" deep anyway. Are you thinking of the 30 gal trash bags?

Sorry to sound obvious, but what about Rubbermaid? My cabinet pull-out fits the Rubbermaid Commercial wastebasket perfectly. It's the Rubbermaid Commercial Wastebasket #2957, 41-1/4 quart (10.25 gallon). It comes in beige, gray or black. Indestructible, and everything cleans off of it.

Here is a link that might be useful: Rubbermaid Commercial Large Wastebasket 2957

Try The Container Store online and quickdrawers.com.
If you don't see what you want on quick drawers, ask to speak with the owner, Keith Barker. He's super helpful and can probably point you in the right direction as some of his pull outs are quite large and come with trash containers.

Perhaps storage containers. They are available in many sizes and quality. I have a pet food storage that is the size you need. Check these too. All have tops that can be removed.

Samlawn,
Much as Ginny20 says above - I find that the 13 gallon bags work perfectly in my 36 quart can. It gives you enough "ease" to tuck the top of the bag around the rim of the can, plus a little room to cram in extra goodies on the way to the curb. My can is by RevAShelf which my cabinetmaker provided with my trash/recycling pullout. Sounds like yours is similar. If your goal is to accommodate the 13 gallon bags I think the 35 or 36 quart (9 gallon) can is what you should be looking at.
HTH, Ruby

Thanks for the tips! I think I'll try a 35 quart and see how it goes.

Actually, on RevAShelf, you can just buy containers, and they do have the 50 quart (13 gallon). I'm looking to do a double trash pullout with the 50 quart size, so noticed this page in my search...hope it helps!

Here is a link that might be useful: RevAShelf containers