More exposure on the bus than if you SELF drive. But "exposure" on the buses really just means experiencing 3-to-a-seat. Hiring a driver who is talkative and friendly, finding a seat companion on a flight who is the same--with the greater possibility that those people will actually be able to speak in English rather than simply share smiles--is perhaps more meaningful exposure.
I would never hire a driver for an entire trip, or around town, but my real reason for riding the bus is that I'm cheap. I know that the exposure I'm getting on the bus is not high quality--the conversations go nowhere, and there's basically a lot of staring that I sit through, trapped. Hiring a driver from point A to B--especially when the road is as rough as the one between Gondar and Lalibela and not particularly scenic--means you have about 7 hours to get to know one person really well, and be taken to his favorite rest stops along the way.
I ended up sitting next to only foreigners on my flights in Ethiopia, but of course other than those 5-6 people everyone else on the flight was Ethiopian--so as LizaD says, of course you are meeting the locals. Even people waiting in line to check in were chatty. On my last trip in Myanmar, almost everyone on my flights were the well-off locals, and they were still just as friendly, spoke English more fluently, and yes...invited me to visit them at their homes. I think it's perfectly possible to travel on all types of transport without closing yourself into some sort of tourist bubble...it depends on your attitude.
Back to OP's query: check with TESFA. If they happen to have some clients going to Gondar from Lalibela or vice versa, they might be able to group you in. When I did this, it was 600 birr because the driver was already in Gondar and had to return to Lalibela anyway (half price) and another trekker came along (half price again). I was also trekking with them, but I imagine they would do it for you in order to save everyone some money.