I am on a H1B visa and i fly Learjets for a company in the southeast. The H1b1 application is fastidious and long. The denial of it is a possibility (don't forget the 1000's of us pilot on the street).
Also don't forget the title of the H1B1, it's called speciality occupation, in other words, what makes you more specialized to fly an airplane than an american. It could be a college degree, it could be languages, it could be that you are an excellent cook, whatever. YOU NEED TO STATE THAT YOU ARE EXCEPTIONALLY MORE QUALIFIED THAN A CITIZEN. That's it. It helps also not to be a citizen of one of the countries on the terrorist countries watch list.
Hope this helps.
LearjetGA