When Bourne reaches Vegas airport, Heather clears his passport for him which prevents him from being detained at immigration. How did Bourne know that he would be cleared?
He didn't. Watch his body language in that scene - he is tense and then surprised.
However, he had no choice but to trust Heather Lee and so he went. Seeing previous Bourne movies would show he would readily make himself a plan B if he encountered a problem.