Motorbikes in general do not need an e-vignette.
All other driving school vehicles do need a Bulgarian e-vignette, just like any other vehicle up to 3.5 tonnes.
Vehicles over 3.5 tons must use the distance based toll system (BGTOLL)
Related articles:
What is the BGTOLL system (distance based toll)?
Can I buy multiple Bulgarian vignettes at once for a vehicle fleet?
What vehicles need a Bulgarian motorway vignette?
Where can I buy the Bulgarian motorway vignette?
How much does a Bulgarian motorway vignette cost?