I don't think you can rely on bus service to DS. Not all the hotels have resumed bus service to DS. Those those that have bus service might not run in the morning, at times that work for you. If everything aligns perfectly, non-Disney run hotels drop off at the West side of DS, near Cirque. You'll have a bit of walk getting to Disney bus area.
Ride Share from you DS hotel to TL is the way to go.
BB is not currently open. At one time bus service from at least some resorts to BB involved a transfer at the AK.