Hey Cowboy,
First of all, welcome to GreekChat! I'm glad to know that you're interested in Greek Life, and you've definitely come to the right place to find out more and to ask questions!
I'll be very honest with you, rushing as a senior is difficult on many campuses. Fraternities are looking for members who will bond with their brothers and be an active participant in fraternity events - that includes social activities as well as philanthropic ventures. So, the fact that you're going to be a senior may be a barrier because you aren't going to be an active collegiate for very long. HOWEVER, I would strongly encourage you to rush and show the brothers that you are interested in them and committed to being an involved member.
Tell them upfront that, yes, you're a senior, but that you really feel that you have a lot to offer the fraternity - and give examples! Do you have a good GPA? If so, point that out. Academics is a big part of Greek Life.
Are you involved in extracurricular activities? If so, tell them about it! Fraternities are looking for men who will be leaders, men who will give back to the community and be a good example to brothers who pledge after them.
Also, point out that you plan to be an active alumnus once you graduate and plan to be a lifelong, dedicated member of the fraternity. Showing the guys that you aren't getting involved just for a year of parties may help you get a bid.
I say GO FOR IT! Show your enthusiasm and prove that you are serious about joining. And keep us on GC updated!
Good luck!
Carrie