I'd looked at the Wargames Atlantic Germans for Bulgarians too. It seems more down to how you want to represent the webbing on whether those figures would be suitable. I'm sure that the Bulgarians also used some form of Stalhelm as well making using those Germans easier. Additionally that you aren't just repainting some WWII era Germans makes them using non-original Bulgarian figures less of an issue than you tend to see with those using other figures to represent other Nation's uniforms. As you see with folk thinking they can get away with say painting some Soviets up and calling them Romanians. But I would consider mixing in some Bulgarian specific - or at least not so commonly modelled German equipment.
Sourcing alternative Machine Guns - even if its Brens done up as Czech guns would help. They did use the MG-34 of course. But Some ZB vz.26 would be more visually interesting (Colonel Bills Wargames Emporium does loose brens). I believe I've seen loose MP-18s too, which could work as stand ins for Czech ZK-383s. Though the WWI uniforms would be different enough from bog standard Germans that you could get away with MP-40s if they're easier to source (my main concern would be the Wargames Atlantic figures having the right pistol grip holding arms. They'd have plenty of rifle ones for the ZK-383s). The same would go for support weapons. You may be able to modify the MG-08s which come with that set as Schwarzlose Machine Guns for instance - or just one of the Great Escape MG teams.
I'd had a go at making some of those Bulgarian helmets in the past using Warlord Soviet ones. Its a process of shaving down some areas and add more prominent rims to others (along with some bolts). For a platoon's worth of figures that's time consuming, though even a few mixed in would be enough to again help stepping away from the figures being repainted Germans.
I suppose vehicles is also a way to sell the force. Whilst Germany used all sorts of vehicles - most Wargames go for the more common ones. So perhaps field a few more unusual vehicles with obvious Bulgarian markings.
Sorry if this is coming across as a primer more than me just spit balling a bit. You aren't the first person I've came across this week wanting to do Bulgarians, ah, but it does help at least that you're looking for at least historical accuracy by going for similar uniforms.
Oh, and you could always do some Bulgarian paratroopers. They were pretty much German ones barring different helmets, light machine guns, and camouflage pattern. They didn't make any actual jumps either - so would just be an infantry force.