A visit to the U/RTA website will help you out. I actually ran across your post and this entire forum by accident doing a google image search for U/RTA displays/portfolios for scenic designers (I was looking for interesting ideas).
U/RTA pretty much says in their paperwork that you should be looking at doing graduate work as they have very few other opportunities. The one that comes to mind off the top of my head is Blue Man Group. Pretty much everyone else is a University.
If the grad schools do like you, they usually give a full tuition waiver and then a stipend to cover living expenses. All of my friends who graduated before me (all designers admittedly) are living off stipends while having their tuition waived - in exchange they work a job at the school teaching an undergrad course or working in the shop doing paint or carpentry or stitching or something related to their design field.
First deadline to apply for designers was today, and SM's were back in October. Now you have until December 1st, but you have to pay a late fee of $10. I believe you'd be forking out $85 plus $10 processing plus $10 late - so $105.
You'd have to prepare a common packet and send it the places that are offering in your area. A friend of mine is an SM but going for Directing and already has her packet returned - no sign of a non-University in the common packet listing she got. The list also breaksdown where each school will be (Chicago or New York) as well as the position being offered and an idea of their stipend/waiver offerings. They also include admission information like if you need to take the GRE or if there are other requirements they want for your common packet.
For Directors she got a list of plays that U/RTA uses/recommends for critical discussion and some schools use it, others don't. Those schools sometimes list their own. She's going to spend Christmas break learning like at least 6 plays. As a designer, i'm going to be hashing out the rest of my design portfolio both physical and digital.
I like to think of U/RTA as a schmoozefest where people will hopefully throw money at me for all the hours i've put in for undergrad.
In any event, hope all goes well for you whether you attend or not.