Why is JetBlue's IATA code B6?
I don't know, but ...

If you look at the IATA application form you will see there is nowhere for the airline to indicate the code it would like to receive.

I imagine many new airlines might indicate a preference in an accompanying letter (e.g. they would like a code starting with a specific letter)

If you look at the allocated codes you can see that, initially, some attempt was made by IATA to make the two-character codes mnemonic 

AA = American Airlines
BA = British Airways
etc


However if JB was already allocated, it is reasonable that the IATA
staff would look for an available code starting with either J or B.
Since the Blue of JetBlue is more distinguishing than the Jet part of the name, the IATA employee may have started with B and noticed that the following were already allocated

B1 Bravo Passenger Solution Pte., Ltd. 
B2 Belavia 
B3 Bhutan Airlines dba Tashi Air Pvt L 
B4 ZanAir Limited 
B5 East African Safari Air Express Ltd.


(note I have not checked dates these codes were allocated but the hypothesis seems plausible to me)

The last two are puzzling but perhaps they changed their names (perhaps as part of a takeover, merger or split). Airline codes do get reused. For example, B5 was used by FlightLine before it went out of business.

Then B6 would be the next available code.