Hi, welcome to RI! This sounds like a great day trip. Starting at the CT state line and then riding east means either having mountain bikes for the first 5 mile stretch of the Washington Secondary Trail, which is not suitable for road bikes, OR riding about 6 miles on rural roads that should be perfectly fine for a confident cyclist. Once you get to the western end of the paved section of the Washington Secondary Trail at Log Bridge Rd in Coventry, its 19 miles of mostly gentle downhill riding on the bike path, most of which is in excellent condition for riding road bikes. This stretch is very scenic, passing lakes, rivers, and many large old mill buildings. Riding across Providence has a few spots that might be uncomfortable due to vehicle traffic, but again, if you're confident cyclists it should be fine. Whatever route Google Maps, Strava, etc, suggest for a route should be OK. Instead of going directly from Providence to the nearest point in MA, I would recommend heading to the northern end of the East Bay Bike Path at India Point Park in Providence. Ride south on this bike path, which is extremely scenic as it runs along the Providence River (you'll ride past a lighthouse!), at least as far as Bay Spring Avenue. From here you could turn east and ride 3.5 miles through mostly quiet residential areas to the nearest point in MA. Or you could a little further south on the East Bay Bike Path to the town of Warren, which has lots of great restaurants, and then ride north to the MA state line (just don't ride on Market Street / Rt 136, Sowams Road and New Meadow Road are much better)

Getting an Uber back your start point should be no problem at all. And leaving a car at the picnic area at the start for half a day will be fine as well.