Looking for some advice: I've been pumping and bottle feeding our 3 week old (who refuses to nurse…

Looking for some advice: I've been pumping and bottle feeding our 3 week old (who refuses to nurse normally) and although pumping is uncomfortable and sometimes painful I don't want to formula feed unless 100% necessary. So here's my issue sometime when I pump at night my nipples will bleed a little and will get into the breast milk. Last night I had to dump 5 oz out because it was totally pink. My question is weather I have to dump it or not? Everything I've read has said it's ok if they ingest a little blood but I don't want a vampire baby or to make her sick or upset her stomach. Has anyone else had experience with this? Any help will be greatly appreciated.