I had that for about the first two trimesters at least. It seemed like every time I blew my nose there was at least some blood, but I never got an actual nose bleed. It's mostly gone away now, I'm 35 weeks.
I'm 39 weeks and had nosebleeds all the way through. Some really heavy.
I've been told it's normal. Just the extra blood in your body and weak capillaries in your nose rupturing. I have had a blocked nose every morning throughout pregnancy and sometimes it has blood, sometimes not. Just pinch the bridge and keep your head forward when you do get bleeds. It'll soon stop. :-)
Nose bleeds are common during pregnancy. I also that problem because I have sinus issues even while I'm not pregnant. Pregnancy made it worse.