BAS requires you to make the deposit first, then contact customer service and request the bonus. This can actually be done through the chat with the automated prompts on the website. I ended up getting credited with the NFL 150% free play bonus pretty quickly the other day, without having to talk to anyone.
I'm generally not a fan of having to make a deposit without confirmation of the bonus before putting in the funds. I've had that backfire on me at other places in the past. But the two times I've deposited on BAS and requested a bonus, I've received it right away without too much hassle.