I'm a new archer as well, and the things that help me are concentrating on breathing and form. I mean really, really concentrating. If the shot doesn't happen naturally and smoothly, don't be afraid to just let down and start over. As time goes on, things get a lot easier and more natural. Also, for me it helps to break the monotony regularly and shoot from various positions. Seated, kneeling, twisted around, etc.
I'm sure you'll get some great advice from the more experienced guys here, but that's some of what's helped me get better and more confident as a new archer. Good luck and have fun!
Are you trying to hold the pin on the bullseye the whole time. You will need to float the pin. It won't sit on the bull the whole time. Also maybe look at shooting less draw weight or make sure your form is correct. But concentrate also. Slow the breathing also. Nothing wrong with a faster shot. As long as you hit where your aiming, I would use that technique.
Rushing the shot can lead to bad things and it is a bad habit to have....One of the things I've seen that cause some people to rush the shot is a bow that doesn't fit them right at all or really bad form that just makes it uncomfortable to shoot so they try to get the arrow off as fast as possible. Shooting a poundage that you can really handle "just because you can pull it back doesn't mean you can really handle it" and having the draw length right are 2 of the main things you can do to improve your shooting.