A budget of around £25 should get you a decent one bed, furnished place, certainly around Sunny Beach area. Varna, close to beach is more expensive. We have just bought an apartment in a brilliant complex 6km out of Sunny Beach so away from hustle and bustle. Quiet, well maintained complex. We paid 26,000 Euros for a good sized one bed, furnished resale (never used). We stayed there last summer in a friend's apartment and loved it. Can walk to nearest village and its still 'Bulgarian', or can go into resort. There is a regular shuttle bus for around a Euro each way I think. Legal fees and taxes came to around 800 Euros - I split the purchase costs with the seller. You don't need a company for an apartment.
There are a few apartments for sale on the complex and can highly recommend it.