Can I sit for long amounts of time 5 weeks post BBL? I'll be home for 5 weeks to recover but need to fly 11 hours to college

There are no hard and fast rules on when to fly or how to sit when flying after a BBL.  Most would recommend a week or two before flying.  This question is best answered by the PS who performs your BBL as he/she will have his/her own post-op guidelines and will be aware of any complications you experienced during surgery and post-op.
The main risk that would be the most serious in sitting on the plane:  development of a blood clot in the legs that can then migrate to the lungs. Sitting for long periods of time puts you at higher risk due to being stationary.  You can obtain a letter from your PS requesting that the flight attendant allow you to stand when the seat belt sign is off, and walk the aisle every 30 minutes. Use your pillow to take pressure off the buttocks and place it under the thighs.  Pressure on the fat, etc. are also possibilities. but it should not impact fat survivability provided that frequent breaks from sitting are taken.
I have developed a modified sitting protocol that seems to work well for those going to school and those who have desk jobs.  I recommend that my patients minimize sitting, even with a pillow, for the first two weeks.  If they must sit, every 30 minutes or an hour, they should get up and stand for a few seconds to take the pressure off.   This reduces the chance for fat necrosis. I usually recommend about 6 weeks before sitting without a pillow. After 6 weeks the fat has revascularized, and they will have a very good idea of their final results.  
Five weeks recovery at home is reasonable before returning to college 11 hours away.
Kenneth Hughes, MD, Board Certified Plastic Surgeon
Los Angeles, CA

You should wait at least 2 weeks before sitting without a support cushion and sleeping on your back. Sitting with no support too soon can harm the newly moved fat cells.

Dear Tyyy77,I instruct my patients not to sit for 2 solid weeks. We provide them a specialized pillow that our patients can sit on during that time. They can sleep on their stomachs or sides. Fat viability depends a lot of surgeon technique. The fat has to be placed back into the buttocks as soon as possible so that it has a greater chance of survival. It has to be placed carefully so that not too much fat is placed in only one area.Every plastic surgeon has his own postoperative protocol which he recommends to his patients. I would suggest you to discuss this with your plastic surgeon.Daniel Barrett, MD, MHA, MS 
Certified, American Board of Plastic Surgery  
Member, Am. Society of Plastic Surgery