Jim's estimate of a viable cost is about right, though you may be able to charge more to a non-local who will find it easier to deal with an English-speaker.
You probably want to check who is already offering such a service. There's a Brit based in Dobrich who posts in the Facebook groups, acting as an agent selling ex-expat properties and also offering property maintenance. No idea what he charges. Our "spare" block of land had become a jungle, a bit too much for me to stay on top of when I only have a week at a time to work renovating the house and keeping the main house garden weed-free. I was desperate enough to be willing to pay Brit prices, and he never got back to me!
Since then I found a local who would do the most important part of it for me. Our neighbour said to pay him 50 leva, but when I went to pay him he said it was too much and he'd only accept 25 leva. (Our village is blessed with some very honest people!) We agreed he'd do it again the following month to make up the 50 leva.
But many Brit property owners won't have such helpful neighbours or be able to arrange it themselves in Bulgarian, so there should be a market. I think the main challenge could be getting the service known. It's probably not actual expats living in Bg who would be the main customers but those who own a house but don't live in it. There are a couple of beautifully renovated foreign-owned houses in my village that never get visited and the gardens are overgrown. Or the people who have a house but only come over for a few weeks a year and don't want to spend all that time weed-whacking. Those are probably your target audience, who'd pay for someone to go in monthly to keep the weeds down and make sure no windows have broken or tiles slipped.
But I'm not sure how one would promote the service to that group. They might be lurking on forums like this one or the FB groups. Local agents selling houses and mainly targeting the Brit market may be willing to promote the service for a reasonable fee. The Bulgarian language FB groups might be a place to promote, too, as that's where I'd look for local services.
It's potentially a viable business, especially along the coast and in Varna region. Probably less so in the more rural areas where the less-wealthy expats (like us!) buy. But it depends on the demand for the service, the competition, and how you can promote it.