I had a licensed electrician replace my main panel and also install a subpanel in my garage. At the time I knew nothing about electrical, and now I know just barely more than nothing. I have recently learned that the ground bar and neutral bar should be bonded. I have examined both my main and subpanels and determined my bars are not bonded. Should the ground bars in both my main and subpanels be connected?
Neutral and ground should only be bonded at the service equipment. This could be at the service drop, the meter, or the service disconnect (250.24(A)(1)).
Looks like the neutral is bonded in your main panel, via the bonding screw.
The second panel is then fed using four wires, to keep ground and neutral separate.