Okay I have answered a similar question to this so I'm just going to repeat what I had said in that previous question because I still hold the opinion that what I said is true.
Right now, what you are asking here is for a label. The only person who can truly label you is you. No one else can tell you whether or not you are lesbian or bi or whatever. Only you can determine that for yourself.
So let's look at my personal experience. Thus far I've only dated guys but I have had crushes on both guys and girls. I have found that looking at girls is more arousing to me than looking at guys (I honestly think that female bodies are more attractive), but being with a guy and having an emotional and mental of connection with a guy is more arousing to me than being with a girl. Overall, I prefer guys over girls but I don't dismiss myself as being straight because I still find girls sexually attractive. But I wouldn't consider myself bi either because I just don't think that that label suits me (even though it probably does for most intents and purposes). I see me as simply me and I've grown to accept that.
That's why I'm going to leave it up to you to decide what you want to be considered as, but I'll give you some suggestions on how to think this through. If you don't agree, then by all means ignore this if you want to because this is just my opinion. Anyway, most people who are educated about different sexual orientations don't think sexual orientation are boxes that people have to be put in. Most people would say that it's a line spectrum (similar to the Kinsey scale where 0 is straight, 6 is gay, and X is asexual). You can learn the general parts of it here (http://en.wikipedia.org/wiki/Kinsey_scale) or you simply Google it.
Although personally, I don't quite agree with the whole idea of the spectrum or the Kinsey scale entirely. I honestly think sexual orientation consists of three types of attraction (sexual, emotional, and mental) and they can each vary on their own individual spectrum however they like depending on the person. In other words, I think that each type of attraction should have a spectrum or a Kinsey scale of their own. These three types of attraction are not dependent on each other, meaning that just because one of them measures high for a specific gender, doesn't mean that all of them do. For example, a man can be sexually attracted to mostly males (a 4 or 5 on the Kinsey scale if you want to think about it that way), emotionally attracted to only females (a 0 or 1 on the Kinsey scale), but mentally attracted to both genders equally (a 3 on the Kinsey scale). There could be someone who is not attracted to anyone sexually (X on the Kinsey) but may have mental or emotional attractions. Or for me, I am sexually attracted to mostly females (about a 4) while being mentally and emotionally attracted to mostly males (about a 1 or 2).
So if you think that the label bisexual suits you because you find both sexes attractive, then by all means own up to it and be proud. If you find both sexes attractive but don't really like or care about labels, then don't call yourself bi (although it does help for simplicity's sake when you talk to those who are a bit more ignorant about sexual orientation) and be proud of that. Yeah people will probably label you as a bi if you like both guys and girls but whether or not you want to see yourself that way is up to you and is the only opinion that matters. But don't worry, you are not alone in this and what you are going through isn't wrong or weird. This is perfectly fine and I hope that I made part of the journey easier for you.