The Bears are doing a good job of running the ball, which means they should see some simpler zone coverages if they throw on 1st or 2nd down.
3rd down is an entirely different story, anything over 3rd and 2, which is not a real run threat, you will generally see man coverage and pressing all the receivers at the line to disrupt routes and give the pass rushers more time. And the Bears receivers are just not good enough to get much separation, other than maybe the TE Miller with a matchup advantage. Put a safety over the top to help cover Miller, bring a blitzer and lock up the rest in man, and that's a pretty good formula to stop the Bears. This is why we are seeing so many attempts to Cohen, he is probably the only matchup advantage against a LB that can get open, he is just inexperienced. So those are the Bears top 2 targets, Miller and Cohen, the only guys who can consistently beat their man.
But the Bears aren't throwing much on 1st or 2nd down, they are rushing the ball because it has been effective and this is their identity.
As Trubisky gets more comfortable, we will likely see some more pass attempts on early downs to take advantage of some softer zones. It will keep the defenses more honest and allow for some less contested receptions.
But 3rd down is going to be a real bitch. And I don't see it getting better anytime soon because we don't have the personnel, especially on the outside.