Bitcoin was founded at the end of the "great recession", so we don't really what will happen if a recession hits....
I could see two scenarios. People cash out their bitcoin to dollars so they can pay their bills, driving the price down.
Of, if the dollar declines and/or people are getting out stocks, there is a buying spree, a flight to safety or hard assets ... like we see with gold buying in a recession.
I'm hopeful of the latter.
Actually, gold price dropped by >30% from Jan-2008 ($1068) to Oct-2008. Gold resumed its growth only mid-2009 when stocks started to rebound.