I'd imagine sometime around 1969-1970, actually. I believe he'd take the fastest possible withdrawal plan without destabilizing South Vietnam (there were several plans on the table at the beginning of the Nixon administration, including a run-for-the-hills option). I think it's also highly possible he'd implement some sort of bombing campaign against NVA/VC positions in South Vietnam (mind you, not against North Vietnam itself). I think it's also likely he promises the South Vietnamese to reintroduce bombing if it seems their independence is threatened (whether he'd follow through with that pledge I'm not sure). I also think Henry Kissinger manages to work his way into the Kennedy administration so I'm not too sure RFK's approach would be all that different.
Bobby was in favour of a peace settlement and since the 1973 Peace Accords was essentially the same one on offer in 1968-1969, I think it's likely he takes the deal sooner than would Nixon IOTL.
In such a timeframe, you could see a peace agreement being signed in 1969 followed by a gradual withdrawal through 1971. However, I imagine that Saigon would fall by 1973 if not earlier.