Hi, Welcome to the site!
Prepare to become addicted to bowfishing.
In IL bowfishing is covered by the Aquatic code (fishing), not hunting. You need a sport fishing license.
There is no general bowfishing season statewide. However, in the fishing regs book you'll see lots of 'site specific' regulations. Many of those bodies of water will either not allow bowfishing or there might be special regs for bowfishing such as a season. If you're not sure about a particular body of water, you can always ask us here. We'll find out for you.
Keep your bow inoperable while it's in your car/truck. (It's debatable whether a fishing bow needs to be in a case in your truck, but it's easier to play it safe than argue with a CPO)
Once you are on the water, you can shoot your bow while the motor is running. Since you are fishing, it doesn't need to be in a case. We have a document from the IL DNR to clarify this. Let us know if you need a copy.
I would advise you to only carry bowfishing arrows when bowfishing. A CPO would be suspicious if you had someregular arrows with you.