Is there a way of seeing how much bandwidth a program is using? If it could tell how much bandwidth each tab of Firefox is using would be even better, but an even bigger ask, I realize.

Occasionally my bandwidth gets taken up completely, even though I can't find anything downloading. (Sometimes I close some tabs till it stops, but I'd prefer another solution).

An alternative would be to temporarily block an application from the internet and see if that frees the bandwidth. That sounds more likely to be doable, but is there an easy to use implementation of this idea?

What version of Firefox?

Tabs don't take up bandwidth. Bandwidth refers to network traffic speeds. A web browser requests a page, receives the content from the server once and displays it. There is no constant connection taking up bandwidth.

You may be confusing bandwidth with applications taking up processor time or ram.

If your router is capable of forwarding netflow information you could look at port traffic. I would bet that most home routers do not handle this, your mileage may vary.

A great tool that incorporates much of this type of diagnostic information is OSSIM.