These are both valid questions, with the former becoming an FAQ, but regrettably, do date we've been unable to get an answer on either. Bill's management seems to be playing its cards very close to its chest (perhaps they don't know yet, either, or if they do, they're not telling their staff), so repeated calls continue to meet with an "I don't know" response.
We suspect that the free-shuttle service may well continue, since Bills's is owned by Caesars Entertainment, not Boyd, so was evidently was picked as a convenient pick-up/drop-off place to enable customers of the latter's two off-Strip properties to have free access to/from the Strip, as opposed to being a commercial link to a sister casino. Bill's imminent closure doesn't affect the fact that the Gold Coast and Orleans, whose locations might otherwise be a deterrent to some, want to make sure visitors without transportation can still get easy access to and from where the main action's act.
As to the Tix4Tonight office, this we suspect will close, although no one has informed its staff either way, as yet. Since it's located inside Bill's, and the renovation plans for that property are to be all-encompassing, we imagine the construction company will not want member of the public coming and going while the work's underway. We'll keep an ear to the ground and pass on definitive answers to both questions as soon as we know for sure. In the meantime, here's a link to all the other Tix4Tonight locations.