Not sure what you mean there, back of what? Your back or the back of a cart?
The carry/stand bags are a nuisance to put on a push cart. They just don match up well. So I'd suggest a cart bag over a carry bag if you want a push cart. I have a Sun Mountain C-130 cart bag which has LOTS of room in it, but it's
big. Must have named it after the airplane. There are a few push carts here:
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The three wheel Clicgear is very nice. Not cheap but durable and easy to push, also easy to fold up. The 4 wheel Caddytec is also a good model for the same reasons. One caveat with the three wheeler: make sure the front wheel can be easily adjusted. If it goes wonky, it can be a bear to push around. Also, the wider wheels of today are much easier to push than the older skinny wheels like I have on my 15 year old Bag Boy.
Hope that helps.