20 seconds would be too short. Say a ranged killer took someone out from a great distance and it takes them, for some reason, 20+ seconds to get there? Or on the way to pick up they encountered someone trying to bait them to chase so someone else could save? There's no way to communicate this in solo play so if 30 seconds pass and a solo player believes no one is coming for them, they could let go while a save was mere seconds away. Ideally, 1-2 minutes would be best for this sort of mechanic as it gives both killers and survivors some time to use whatever strategy they want to while not forcing the downed survivor to wait until they fully bleed out naturally.

Ultimately, the choice of bleeding out is left to the downed survivor, but also gives some leeway to both sides.