All the European Health Insurance Card (EHIC) gets you is the care an EU country's citizen gets, the extent and quality of which varies from State to State.
In a country such as Bulgaria this could be very basic and in poor conditions, so there is no substitute for proper travel insurance, that covers you for all the activities you are going to undertake on your holiday, and repatriation which can cost many tens of thousands of pounds.
I would suggest that you actually carry the E111 card with you at all times as the "Tonight programme" (ITV) reported on this last year and some European hospitals would only treat you if you actually had the card with you when you arrived at the hospital.
the EHIC isnt valid in bulgaria (apparently,this is what we have been told by leaflets, travel agents, ski companies, etc..) you have to pay for the full amount if you have an accident. Most medical centres in ski resorts are private anyway so the card will mean nothing
I was taken seriously ill in Bulgaria a few years back (diabetic problem) and spent 10 days of a 2 week holiday in hospital in Sunny Beach.
The facilities were so basic it was unbelieveable (my drip was mounted inside a sawn in half Diet Coke bottle) but the attention I received from the staff was just fantastic.
All they asked for was my travel insurance details and they did the rest - I never parted with a penny.