Looking for a connection from Christiansburg VA to Bristol VA without a driver's license. Long distance ride share? Public transportation? Willing to link a few shorter stretches together if needed. Trying to avoid a 6 hour route that's been suggested, as the distance is half that. Thank you in advance!

That's a problem as it is a straight shot on I81 driving. I don't know anything about ride shares, maybe there is some app for that. And the problems is those are not major cities, so yiou are never going to get major bus/train routes between them.

One method is to take the bus from Christiansburg to Roanoke, which is a fairly major city in that area, that takes about an 30-60 minutes. Schedule is on here (the Smart Way Express bus).
https://smartwaybus.com/swx.html
You need to catch it at the Exit 118 Park & ride. Now that lets you off in Roanoke about 1 mile from the Greyhound bus station (at VCTRI). Valley Metro also runs a trolley between those two points that is free. Here's the schedule and map.
https://valleymetro.com/trolley.html
Get out at the stop on Kirk Ave which is about 1-2 blocks from the Greyhound bus station (stop 2).

Then Greyhound bus 1511 goes from Roanoke to Bristol, takes 3:20 hrs.
That's the only way I can figure it out by public transportation, but all in all that may take almost 5 hrs.

And I don't know if the schedules mesh. The bus from Roanoke to Bristol is only at 8:30 am. The Smartway Express bus does get into Roanoke at 7:30 am, so that hour should be enough to get to the Greyhound station. The Smartway bus Exit 118 is about 2 miles from Christiansburg so I guess you'd do a taxi or Uber for that. You'd arrive in Bristol at 11:50 am.

so you're talking maybe 6:30 am to noon all told travel time, not much better than 6 hours, although not all in one piece. If you don't mind spending time in Roanoke or something, that could work. I'd rather do a 3.5 hr bus trip than a 6 hr one, that's for sure. That's presuming you found some 6 hr bus trip, I don't know the comparison. But you are just not going to find some streamlined quick public transportation method between two small cities like that.

Hope you found something. Not sure if you are from the US but unfortunately, we don't have good regional transportation infrastructure. We rely heavily on driving.

A rideshare would be the quickest option if you can work it out:
https://ridesolutions.org/new-river-valley/

I'd also look at Facebook groups for Rideshares to specific places. Since Va Tech is fairly close to Christiansburg, you might be able to connect with a carpool going your way via a Facebook group.

But I wouldn't hold my breath on that option. You'll probably need to take the 6-hour option or, if you possibly can, rent a car.