I'd call your Dr and get an u/s done. Red bleeding is always cause for getting checked out. So don't delay.
In regards to bedrest, it's tough to say. Some Dr's put women with subchorionic hemorrages on bedrest, however, my Dr stated there is no good data to suggest it helps. However, if it helps you feel better, like you're doing everything you can, then yes, take it easy. And drink LOTS of water to try and calm down your uterus.
Most of all though, get an u/s.