It sounds like what Larry Knopp pointed out, the fuse on RUMBA is the same as RAMPS; the bed fuse is rated for 11 amps.
You might want to consider driving that kind of load from a solid state relay - they're quite cheap and handle huge currents. For example,
this one will handle up to 40 amps (though leave a safety margin, see below). You can get these in lots of places, the important things to look for is that it's DC-DC (most are DC-AC, so you can switch a wall plug / mains current from a low voltage, but in your case you want to switch DC voltage). Because the input voltage is 3-32v, you can either hook up directly to the pin on the microcontroller (5v = on) or hook up to the heated bed output (12v/24v = on) and it will work fine. I would prefer the microcontroller direct (less to go wrong, no need to switch the high voltage side on), but I'm not sure if the RUMBA has the pins easily accessible.
You should always leave a safety margin when working with these currents - for example I have a 200W heater and have calculated around 100W for other things (hot end, motors, lights, etc). My power supply is 600W, which gives me a 50% safety margin. One could argue 50% is a bit much, but you should leave at least 20% - in your case I would use a 450-500W for the bed alone (if you're driving your hotend and other stuff, add more!).