I'm in grad school. If you really feel passionate about it, there's a way to make it happen. When it comes to field work - that's what undergrads are for!!!!!! haha
But seriously....I have epilepsy and it was a constant struggle because it doesn't take much stress to make me have a seizure. So sometimes, doing field work, I would have to stop and go sit in the truck for a few minutes until I felt okay again.
What exactly about birds are you interested in? Have you done a search for it?
I used to work at the Cary Institute in upstate New York and they did a lot of bird research there. Most of the profs there were from Texas Tech so maybe search their ornithology site and see if you like what you see.
First things first. Figure out what YOU need. Do you have to stay in the same city? How far can you move or travel for grad school? Once you narrow down your area, think about what you are interested in. A good way to start is to look at google scholar. Search for some journal articles that you find really interesting and look at the authors and references. These are the people you may want to contact. Even if they are too far away or not accepting, they most likely know someone to direct you to.
Most profs will have a grant which will cover your tuition plus give you a stipend of usually around 15000 a year. When you get past everything I just listed, start emailing or calling. If you can find their individual sites, a lot of times they will flat out say whether they are looking for someone. Then you and them can see if you have good chemistry, if your interests overlap etc....
I hope all this works out for you. And as far as the GRE goes....I hated it. It was expensive. And nobody really cared what my score was. I think it's pointless but apparently chairs of depts don't.
And if you are looking to possibly get some experience before applying to grad school,
http://www.wfsc.tamu.edu/jobboard/ go there. They have internships, masters, phd, temporary and permanent jobs etc... It is all wildlife based and they usually have a lot of bird work on there. Plus you can narrow your search to a state or area of work.
PM me if you need anything! Good luck!!!!