I ovulated on 6/18, then had what i thought was a full period on 7/2. on 7/8 i had positive hcg of 231 and on 7/11 had hcg of 539. dr. says bleeding can be normal, but how? isn't cervix closed?

Your doctor is: correct, some bleeding is common and can also be normal. This often gets called 'implantation bleeding' or (worse) 'decidual bleeding' if it happens a little later on; neither term has a concise meaning, just ways of saying "some women bleed early in pregnancy, we aren't sure why." The cervix is mostly closed but not shut tight, this is similar to how you bleed with a menstrual period.