As others have already said, overdrawn bank statements are a big no no. You need to show that, on paper, over a six month period you are solvent, ie more going in than coming out on most of the monthly bank statements. You don't mention whether you submitted evidence of you savings account as well, but if not, this is also something that would help a lot.
You may think that you are solvent, and given what you have said about your savings, I would probably agree, but the ECO would make his/her decision based on the evidence you sumbit and if the evidence he/she is given gives the impression that you are living beyond your means because you are regularly overdrawn, then he/she will normally decide that you probably won't be able to support your fiancee in the UK without recourse to public funds.
Iain.