I wouldn't worry about it, and it certainly does not sound like the bloody show. This pregnancy is my fourth, and for the first time ever, I've had spotting on and off. Starting in the beginning of the third trimester, I have been spotting a bit, and at first it really freaked me out! It was red-pink, not brown, and like you, we also had not been having intercourse. It would start and then stop right away, only to happen again a week later. This went on for about 1 1/2 months, and my OB did an ultrasound to rule out problems with the placenta (everythig is totally fine!).
He said, and my doulas agreed, that there are often cases of unexplained bleeding during the last trimester. For me it also tended to correlate with my overdoing it---like manically cleaning and mopping, for example---but there was not always a correlation. Anyway, since it was just spotting, no one got too anxious about it, and in your case, I guess I wouldn't either. Sometimes it also happens that the baby is just heavy, and the cervix and stuff gets a bit thrashed by the extra weight. Such would seem to be the case with this baby that I'm carrying.
Anyway, just take it easy, lie down a lot, and don't do any extra heavy physical stuff. Even though everything is fine, your body is still under a lot of strain, and more rest now is always a good thing. Try to put your first birth experience out of your mind for the moment---just spotting doesn't mean you'll end up sectioned again!! Rest and enjoy these last few weeks as much as possible. If you get an increase in bleeding or spotting, I'd recommend getting an ultrasound to rule out placental issues (and I am NOT an ultrasound person, but better to be safe sometimes.)