Lianne - Welcome to FlyerTalk!
I fly in and out of BUR at least once a month and I have yet to see a jetway. I also thought the BUR airport link
http://www.burbankairport.com/ might address your concerns under 'Special Needs' but it doesn't.
My best advice is to contact your carrier. I have a feeling that they will tell you that they have a 'lift' that transports wheelchair passengers between the ramp and the aircraft. I am sorry to hear that nobody knew how to use the lift the during your last experience. That is unacceptable and unbelievable that nobody knew how to use the lift including the supervisors and station manager?
As for using LAX over BUR, I would consider the flight schedule. Using BUR may be more convenient that LAX especially during 'peak' travel times -- LAX can be quite a zoo!
Good luck and safe travels!