You might want to post this on the Disney Resorts board to get some other viewpoints. Most of us here (me included) are big fans of offsite rental condos (the value especially if you do an owner rental is exceptional - quality for price, and offsite resorts are really nice). I love having my own kitchen -- even if it's just for breakfast and snacks. My teen is always eating. I love having a balcony without having to pay Disney Deluxe prices. A big hangout area in the LV/DR is wonderful too. And if I have a condo, I pack lighter, as it's so easy to throw in a load of laundry once or twice. I've also done a comparison of renting Disney points from an owner for Disney condo vs. offsite condo rental from an owner, and when I've crunched the numbers, I've found Disney condos to be triple my offsite price and it's never been worth it to me to pay that much more. I've never stayed at Bonnet Creek, but have stayed at other offsite timeshare properties that are in the same general area, but a little farther away -- Cypress Pointe and the Sheraton Vistana Resort. I'm thinking you'll get quite a few responses from people who have actually stayed at Bonnet Creek too on this forum too.
Anyway back to your questions. With the exception of the downtown Disney hotels, shuttles typically have very limited schedules making driving your own car the way to go. I find that it's pretty easy to drive around Disney and driving my own car is faster than waiting for a shuttle even when I'm off property and farther away than you would be. It's not as convenient as the monorail from the POLY to the MK, though, that's for sure. Parking at the parks is $17 a day and if you hop from one to another, etc. you only pay once. Also there is no fee for parking at Disney water parks.
https://disneyworld.disney.go.com/faq/directions-parking/parking-costs/. With teens though who might be going places on their own, I can see that more frequent shuttles would be nice, and that's something you would be giving up. If you're going to be going most places together that's not as big a deal.
The POLY is absolutely lovely, but very pricey. I do love the grounds and vibe there, and if you go offsite you aren't going to get the same kind of theming as you get there. It's just going to be a lovely generic resort, so you have to decide if that would be acceptable to you. Personally, I think it would be worth it to try offsite and see what you think. So many of us after doing this never go back to onsite again. Some people like to switch it up onsite and offsite. And there are others who say never again to offsite.
The people most thrilled with offsite, though, tend I think to have when onsite stayed at moderates and values, and the offsite resorts are IMHO much nicer with way more amenities than those plus they cost less. That makes the offsite choice a no brainer. You're not giving up much. Disney deluxe resorts have IMHO incredible theming and convenient locations that the offsite resorts don't have. I do love that theming, but not for the price and choose offsite. But I could see you missing that if going offsite.
Disney does have their condos too. And there is the option of renting Disney points and staying at a Disney condo at one of the deluxe property locations. If you want the space that option and offsite are probably your best comparisons. And then the choice becomes am I willing to pay three times as much to be in a better themed resort, closer location, with the Disney transportation or do I want to try offsite (give up that and go for the incredible value that many offsite visitors rave about).
Oh and early morning traffic -- It's just not there. Road are pretty empty in the mornings. People sleep in on vacation.