Another recession means keeping the interest rates lower for longer time - so people would look for alternatives to fiat currencies such as Bitcoin, but honestly I doubt the US is going through another recession - they are aiming for raising the rates which would shift movement towards the USD and not towards Bitcoin.
I don't think many people would flock to bitcoin even if the US dollar was in trouble. It needs to be a readily acceptable method for payment for it to be treated like a legitimate alternative to the dollar, and it's not that way yet.
If the dollar collapses, people usually go towards physical assets and in particular, precious metals and real estate.
but many will go to bitcoin in this case, and will increase the adoption which will start a series of events that will increase even further the adoption, so the collapsing of the dollar is for sure beneficial for bitcoin
For that "many" to go to Bitcoin they need to know how to use it and be sure about it, which that is still only a small member of geeks compared to the mass of average joe and the rest of the sheeple, if this wasnt' the case Bitcoin usage would be sky rocketing in Greece as we speak, but people is too clueless yet.