Hi.
There are very few surfaced main roads in Sumatra.
From Bukit Lawang if you want to get anywhere, you must first pass through Binjai, from where you have the choice of heading north into Aceh or continuing into Medan. From Medan you can take the road to Berastagi, or to Tebing Tinggi.
In other words, from Bukit Lawang you must drive to west Medan, head south and then up on the road towards Berastagi.
That said, there are certainly many more roads than the main road, and Bukit Lawang has many Karo people because it borders Karo Regency, which shows that people do and have moved without using the main road.
So it's possible to make a long trek from Bukit Lawang to Berastagi on foot (4 days), and I think maybe you could go by motorbike or even by off-road vehicle. But if you did, it would certainly not be more comfortable , cheaper, or quicker, than following the Bukit Lawang-Medan-Berastagi main road.
You can book a tourist bus direct to Berastagi in Bukit Lawang, either per person, or charter your own, but it will still pass through much of Medan, you are only saving time/comfort, compared with the public buses via Medan.