Has anyone flown British Airways from Heathrow to Ljubljana (Slovenia)?

No, I haven't. The last two times I've visited Ljubljana, I flew into Venice which was convenient for me (last time, I got a direct flight from the US to Venice). It's about a 2.5-3 hour shuttle ride from Venice Marco Polo airport to Ljubljana via GoOpti or DRD, plus there may also be buses now with FlixBus and the like. I'd fly right into Ljubljana if it ever works out best for me, but I'd rather get a better flight into Venice if that means a better flight with fewer connections, etc. Maybe next time...

Ljubljana's airport is a 40 minute bus ride north of the city, about 17 miles, the bus is roughly hourly. The bus is only a couple dollars or so. There are taxis and shuttles that will be quicker but will cost substantially more, the shuttle appears to be no more often than the bus.

It doesn't matter what airline you're flying on and it doesn't matter where you're coming from.

The airport in Ljubljana is fine, although fairly compact (after coming from Heathrow, you might actually enjoy it). It's a bit distant form the city, but there are multiple options to get from there to the city. Just allow a little time, no issues otherwise.

Slovenia is a modern, developed European country. The airport is fine, getting to the city is not a problem.

British Airways do not operate any direct flights between Heathrow and Ljubljana. For a direct flight from London, Easyjet flies to Ljubljana from Gatwick and Stansted, while Wizz flies from Luton.

Alternatively, fly into Venice, as others have suggested.