You have already been given some good advice in this thread.
FightinIrish and Roundhead are spot on with regards to being elite at both bodybuilding AND MMA. However, the way I read your post, it seems you just want to try your hand at martial arts/MMA/combat sports. If that is the case I think you can absolutely do both.
I do not know how long you have been lifting. Your post says you are following a 5 day split for bodybuilding, I do not know if that is the total time you have been training or just your most recent regime. You have also mentioned that there is an MMA gym you would like to train at, but it is out of reach due to financial constraints.
Here is what I suggest. First, you must find a gym that you want to train at, can afford financially, and can fit training at into your schedule. Open the phone book/go online and look for martial arts schools, boxing/kickboxing gyms, and Judo/wrestling clubs. See if you can find a location near you. Visit/watch classes. Pick the one you think you fit best, that you can afford, and that you can attend a couple times a week with your school schedule.
You may need to get a part time job in order to finance this. That is fine. Do not pick a gym that costs a ton, and use this as an opportunity to practice time management. I do not know what level of education you are at, undergrad/university, post-grad/masters, doctorate, ect., but regardless time management is important. Working 12 hours a week or so shouldn't put you in a bad spot with your studies, especially if you can find a job that lets you get some studying done at work. For students I would recommend a job that falls into one of three categories:
A. Related to your future career. So future doctors/nurses may want a hospital job. Future reporters might want to do anything at a newspaper or magazine.
B. Pays well/tips-Tending bar, waiting tables, ect all do a good job of putting a high amount of cash in your pocket for minimal time. It is a financial bonus if you are stuck working shifts you would otherwise be out spending money.
C. Lets you combine work with study time. Some desk jobs/night time security jobs leave you with a decent part of every on the clock hour to study. Even though the pay might not be great, it is a time saver.
Finally, shoot for attending your martial arts/fight gym twice a week to start. While this will get shunned by the hardcore set, it is enough to get started. As for weight training, do both combat sports and lifting until one interferes with the other. Then, decrease the time spent doing whichever one you like less. I concede a 5 day a week lifting schedule sounds like it will interfere sooner, rather than later, but 3-4 days a week in the weight room is pretty standard for University athletes.
Now this is not a plan for becoming an elite bodybuilder, or champion fighter. Roundhead and Irish have explained why. This is a plan for getting to do both. If 8 months from now you realize that you would rather box than lift, then you can make that choice. If you would rather snatch, clean and jerk, and front squat than choke, arm-bar, and pummel than you can make that choice as well. Regardless, you will be able to make the choice based on your own experience.
ADDENDUM: I glanced over this post before hitting submit and saw I had miss-spelled "doctorate." That is a bad sign. So...listen to Irish, or Roundhead, or Westdale, really anyone but me.