Getting Downtown from the airport will probably take you about 25 minutes at off peak hours. There are plenty of hotels around the airport .The downtown area has plenty of hotels too and the tunnel is easily accessible from there. The bridge is not too far either.
I wouldn't use the bus for first time landing in my opinion. I believe you'll be directed to the CBSA offices once you pull up the window and they see that you're doing 1st landing. Below is website to the Detroit-Windsor bus.
https://www.citywindsor.ca/residents/transitwindsor/Routes-and-Schedules/Tunnel-Bus-to-Detroit/Pages/Tunnel-Bus-to-Detroit.aspx
I live and work in the Greater Detroit area, and I just tried to request Uber to take me to Windsor and apparently it doesn't work(unavailable). I don't think they have Uber in Canada. I visited Vancouver a few months ago and they didn't have Uber or any ride sharing services.
Getting a rental should be ok. I was gonna get one next time I cross over because they gave me grief about importing my car. I'll let you know for sure in a few weeks but I think it should be ok.