Late September and early October present the ideal timing for dealing with oriental bittersweet. If you have decided to go with an herbicidal treatment this is when the plants are pulling nutrients back to the root system to store for the winter. Treatment will also be drawn into the root system, making it much more effective. If you are pulling vines from trees or uprooting them, there's still time to do so before the berries drop off the vines as you work. They're pretty well attached which should allow you to dispose of the vines with the berries intact. If berries drop on the ground, pick them up and dispose of them.
Speaking of disposing of invasive plants....
Never toss them in your debris pile or in nearby woods. They'll just go to seed and come back to haunt you and everyone else. Ideally plants should be bagged and tossed with the trash. If that is not possible take them to the local landfill. If seeds are dropping from the plants be sure to bag the plants or cover your truck bed or trailer to limit the number of seeds that fall by the road en route to the landfill. Then sweep out the vehicle at the landfill, rather than letting any remaining seeds blow out on the way home.
There's no such thing as free mulch....
If you've disposed of invasive plants at the landfill on Tryon Street, you may also know that eventually a mountainous debris pile is fed into a huge chipper, creating that "free mulch" you can get at the landfill and at the location near the transfer station on New London Turnpike. The potential problem of "free" mulch is that it may (does) contain the seeds from whatever invasives have been disposed of at the landfill. These seeds can be viable for several years. So the price you may pay for free mulch can be increased vigilence and work to make sure any invasives that spring up are immediately pulled.
Skeptical? Here's a picture taken at the landfill last week. Lots of berries here!