As I understand it, BIS is a FTer term, not an airline term. It's the number of miles corresponding to "United Lifetime Miles" in your MP statement.
A lot of people understand this term to mean number of miles actually flown, versus miles gained by promos, bonuses, etc.

Can you think of examples where you take a flight and get credited with more BIS miles than you flew?

And another example of where you get fewer?

Examples I can think of:

• If you fly less than 500 miles (on selected carriers, UA/UX/Ted for example) you get 500 BIS
• If you short-cut a routing, say taking SFO-IAH instead of SFO-DEN-IAH, and it's due to irregular ops, you can get MP to credit original miles
• If you get diverted for weather, traffic, medical emergencies, etc., you still get only the pt-to-pt BIS for the city pair you were supposed to fly, even though you've flown more

A good example of the last one is when I left BKK in 1999, flew an 1.5 hours, then turned around for a medical. Back to BKK, an hour to refeul and take off. That's 700 extra miles of flying!

Other examples?