Drawing a potion isn't an action.
Just to be clear, drawing a potion doesn't normally require an action; it's listed explicitly on the sidebar list of examples of "Interacting With Objects Around You" (PHB p190), which can be done "in tandem with your movement and action". So long as you aren't interacting with another object at the same time, you don't have to do anything special to pull out a potion. A bonus action to draw a potion is actually longer than the core rules require.
Drinking a potion as a bonus action shouldn't seriously change the length of a combat.
Drinking a potion explicitly IS an action, so that part of the question is valid, and on that point, no, this change likely wouldn't change the duration of combat in a significant way. The party might drop an enemy a couple of actions faster because they were able to attack once or twice during the encounter when they otherwise might have had to take an action to heal up; the enemy might deal a little more damage for the same reason; but overall it shouldn't be an enormous difference. There's still an opportunity cost to making this a bonus action, since by 5th level most characters have something better to do with their bonus action than drink a potion.
You probably still shouldn't do it.
This change would make a potion strictly superior to the baseline healing word spell (though admittedly not much). If you're doing this for a specific reason, like the party doesn't have a healer in the party, this house-rule might be a way to relieve that pressure a bit; but generally speaking it seems like an unnecessary change.