I am wondering, in general, how much experience is required for admission into UCLA or USC’s theatre, acting program.
I believe that I have what it takes to be admitted into the school, as far as my academics go.
Where my concern lies is, getting into the program.
I have taken some acting classes, but none at the college level. I do plan on taking all theatre courses this Fall (when I apply to transfer) and I hope be in on of my schools productions.
I have done extra work and am SAG-AFTRA eligible from that.
I have never been on stage in a theatre production yet, nor have I been in any student films or web series.
I work as an actor at a popular amusement park where, I play a very popular character.
I’m also an agency represented, internationally published model and have filmed some fashion films that required acting skills.
That is as far as my experience goes.
What do you think my chances are of getting into either of these programs? What can I do between now and the audition/interview to improve my chances?
Thousands audition for spots in these two acting programs (combined). Look on website for each school. Each program will outline what is required for the audition. Many students that are applying straight out of high school cast a much wider net in regard to applications. Because the top programs are very selective it may help you to apply to more than just two. I would visit both campuses, tour the facilities and set an appointment to speak to admissions counselors for both. Start looking at monologues. Practice, practice. Also, if you haven’t done so, check the freshman admit profiles for the latest admitted class at each school. Start working on your application essays. Also, if you stay in junior college for two-years you may be able to build up your resume with roles in theatre productions and gain some training before your audition.
As for your chances, I cannot speak to the probability of your acceptance. You sound like you are building professional work and you have a strong interest. Also, you mentioned being SAG/AFTRA eligible. I do not believe the BFA at USC or the BA at UCLA allows you to work professionally while you are a student. However, I think the BA at USC does. Speak to admissions counselors in the drama programs to make sure that your plans don’t conflict with their requirements. You may still want to work while a student.
Familiarize yourself with these two programs and research some additional programs as back-ups. If you want to stay in California you may want to look at Chapman. They have screen acting and stage acting programs that you can audition for and they have a great film department (as do the other two schools) so you may be able to work with film students and appear in their productions.
Before your interview try to anticipate the types of questions they will ask you. Why do you want to go to our school? Where do you see yourself in five years? What other programs have you auditioned for? These are pretty standard. If you follow other discussion threads on CC you can find threads where students are discussing their interviews and auditions for theatre programs. This may be helpful as well.
The “chance me” question is pure speculation for anyone that is responding. You would be best served by researching the hell out of all the programs, finding out what is required, and working your rear off to make sure you are prepared grade-wise, essay-wise, audition-wise. The professional work you listed may look nice on a resume but lots of things need to come together to reach your goal. True acting training and experience shows in an audition. High school students from performing arts schools/programs and those that have been involved in community productions COULD have an advantage over you at this point. I don’t know that extra work will help you. However the amusement park work experience could. Being in fashion is nice but I don’t know if that will help you gain admittance in a dramatic arts program. It sounds like you have accomplished a lot and want to do what it takes to achieve your goal so that is great. Best of luck in reaching your goal 
A few thoughts:
BA Theatre at USC - transfers need a very competitive GPA (3.6+) and should have taken a lot of the GE reqs. Make sure the classes you are taking are covered by USC’s articulation agreement to make sure they will transfer credits. There is no audition for the BFA, so if your credits and GPA are great, this is a good possibility. OTOH, USC is a very expensive private university. Many middle income families do not get big FA so it’s good to get that straight with your family before applying and hearts get broken.
BFA Theatre at USC - by audition only. This program, however, is 4-years in sequence. Transfers may be accepted but I believe they still need to attend 4 years at USC. Check this out as above mentioned $$, not to mention extra time, is req’d.
BA Theatre at UCLA. This program is also 4-years in sequence. I’m not sure they take transfers, so better to check. This is a very competitive, by audition major. If you are OOS, the cost is quite high, so be clear on finances here as well.
To answer your question, none of these programs requires a lot of acting experience, but every audition school will b evaluating your audition against those of other applicants. Training and experience can really show up there. If you plan to audition, you might look into hiring an audition coach to help catch you up to speed.
As has been mentioned, you should consider a wide range of schools when applying, those that are both affordable and less competitive for admissions would be very good to round out your list.