The meniscus can tear or degenerate in a number of different ways, and as such, can present differently in different cases. If you can use the treadmill ok then it would probably suggest it wasn't an issue, but then if using a treadmill to run doesn't bring on any of your pain, then it would also cast doubt on it being a bursitis or hamstring issue in my view. Can you run on the treadmill ad infinitum with no pain at all? If so, what is it that you do differently there that you do/don't do whilst running outside?

The fact that your pain came on very markedly and suddenly to me suggests it's not a bursitis. For an inflammation to occur, you would probably have noticed a gradual worsening of the area over time as opposed to a very clear cut, ouch that hurts! What you describe about sitting down and getting pain if you turn your knee in is very similar to a positive test for McMurrays:

Knee Exam (18 of 27): McMurray's test - YouTube

Could you perform the Thesaly test and let us know if that recreates any of your pain, or problems?

Thessaly Test - YouTube

Ignore the squatting man at the start - don't know what is going on there. Have your knee flexed to about 15 degrees and then bend a little more if you can and repeat.