There are dozens of shuttle bus routes in the city.
You only have to be able to read their route inscription on the bus or simply ask people at the bus stops about the direction.
If you decide to grab a cab, you will not go bankrupt, I assure you. A two-hour ride around the city will cost you $20.
Enjoy your ride!
You can also get to Rovenki via Debaltsevo station located in Donetsk region.
But I would still recommend taking a train to Luhansk and then a bus to Rovenki.
There are buses to and from Rovenki almost every hour.
It will take you about an hour to get there from Luhansk (about $2).