Yes (arrival/departure) transport is not as easy as other locations, so train definitely the option IMO. I'd only rent from somewhere else, if that location was also of interest, such that you might spend a few days there as well. FWIW we did drive from Verona to Lago Molveno near Trento. Much of that was on straightforward autostrade, so the driving is straightforward, with decent views, albeit as good as views from a motorway get! Very doable, and Bolzano will just add additional time, not complexity.
Whilst Trento/Trentino does have Austrian influence, we only encountered one person who couldn't/wouldn't speak Italian (at a cartoleria in Molveno). It definitely felt more Italian than Austrian, albeit food-wise felt more midway between the two.
If looking for somewhere that's finely balanced between the two, then possibly that means somewhere between Bolzano and Trento... or perhaps split time across both to *compare and contrast and venture out from each to get hikes etc.
Mid september weather-wise will be very good, though if heading up into the mountains, can hit that point between summer and winter seasons, where ski-lifts / cable cars may only run on weekends (or not at all). Accommodation should be easy to come by and priced on the cheap end of the seasonal scale.
If Trento/Molveno does appeal, I'm more than happy to expand on what the appeal is / logistics (we've done it both with a car, and just by public transport). Hopefully others could chip in for Bolzano / Alto Adige.
* I have enjoyed a couple of such 'compare and contrast' holidays in the past e.g. Melbourne vs. Sydney was the first of these I did, the idea coming from their 'rivalry'.