I was having a nap when my waters broke. when i woke up, my underwear and pants were soaked. The sheet was a little wet too,but it wasn't enough to soak through to the mattress. When i stood up, more came out. There wasn't really that much fluid. My pants got a little more wet, tiny bit on the floor too.
If you would feel more comfortable with a towel under you, then you should do it. Having a spare pair of pants/underwear and some pads with you at work might be helpful too.