If you expect to make over 50,000 leva from your Spanish students should you register for VAT in Bulgaria?
Well, the short answer is: yes... probably. :-)
If you're over the threshold, why only "probably"?
(a) At face value, it's an easy decision: you're either over (or expecting to be over) the threshold, or you're not. If you're way over, then you have to. But many smaller traders prefer not to be VAT registered because of the extra admin involved, and it adds 20% to your prices. But to avoid the registration will involve some "re-engineering" and you have to decide whether the cost of this is justified.
(b) As three forms of re-engineering you could: have 2 entities (your self and a Bulgarian company) so both entities are below the threshold; give classes to two types of learner (Spain/EU and China/non-EU) so your VAT-able EU revenue is below the threshold; simply give fewer lessons, and stay below the threshold. All have their particular trade-offs.
(c) You raise an interesting issue about language classes being VAT exempt in Spain. As far as I know, the exempt categories in Country A don't affect your VAT if you're registered in Country B. I don't think education is similarly exempt in Bulgaria, but it's probably worth asking an accountant. So you either register in Bulgaria and charge VAT (because it's not exempt here), or you could incorporate a company in Spain instead, and have that register for VAT, and then supply zero-rated services (education). The EU supports cross-border trade, so, in principle, I see no reason why you can't incorporate as a Spanish entity to supply your services from Bulgaria.
(d) While investigating your question, I found a reference to a higher 70,000 leva threshold for "distance selling". But I don't know if this applies to goods or services or both. A Bulgarian accountant could tell us.
Personally, I much prefer NOT to be VAT registered, and I would take steps to avoid going over the threshold. You might be delighted to be VAT registered, in which case, no issue.
Separately, lIke @EVTRA, I question whether the best option is to be a freelancer / self-employed. I believe that you should discuss with your Bulgarian accountant as to whether incorporating a Bulgarian company would be more advantageous.