This appears to be the current situation.
Visa Information, the current situation - September 2006
As of the beginning of September 2006, the visa requirements for Bulgaria changed for UK and Irish citizens.
The old 30 day rule has gone, you can now stay in Buglaria for a maximum of 90 days in any 6 month period. This is a rolling six month period as before, you can't have two 90 day periods back to back. You can stay in Bulgaria for 90 days or any number of shorter periods adding up to 90 days, without further documentation being required other than a passport or (when they bring them in) an ID card.
For stays of longer than 90 days in any six month period OR for full time residency, you apply inside Bulgaria. There is now no c and d visas required by British and Irish or other EU member cizitens. There are still these visas for people coming from outside the EU. The days of queuing at the London embassy or of travelling to Romania, Turkey or Greece are over!
You apply for a stay of four months to five years at the police station's immigration office. You may be asked for any of the following documents:
Birth Certificate *
Marriage Certificate *(if applicable)
Proof that you can support yourself and family, this could be bank statements or proof of self employment. *
Proof of health insurance (a little unclear at the moment, could be the plastic E111 form, your old brown health card, or private insurance)
Proof of where you are living.
You should assume you will be asked for the ones with the *. In theory you should get your new residency pass the same day.
After five years of continuous residency you can apply for a permanent residency.
I will try to keep this sticky updated as more news comes in. To keep it simple, please pm me if you have any comments or alterations so I can add them.
Update thanks to Wandy - 9th Jan
The proof of income required was a letter from the Bank saying you had a 1000 leva in your account
They will accept E101 or medical card both have been used by people to-day.
Also you can only get up to five years if you have that time left on your passport!