No, I don't think you can use your EU blue card to do either of these. I could not find any special rights to enter other EU countries in the Blue Card directive.
But the introduction does contain this:
Third-country nationals who are in possession of a valid travel document and an EU Blue Card issued by a Member State applying the Schengen acquis in full, should be allowed to enter into and move freely within the territory of another Member State applying the Schengen acquis in full, for a period of up to three months, in accordance with Regulation (EC) No 562/2006 of the European Parliament and of the Council of 15 March 2006 establishing a Community Code on the rules governing the movement of persons across borders (Schengen Borders Code) (7) and Article 21 of the Convention implementing the Schengen Agreement of 14 June 1985 between the Governments of the States of the Benelux Economic Union, the Federal Republic of Germany and the French Republic on the gradual abolition of checks at their common borders.
That's a bit difficult to parse but basically it means that if you have got an EU Blue Card issued by a Schengen State, you can travel in the Schengen area (actually, that's usually the case with most residence permits issued by Schengen states, not only EU Blue Cards).
Since the text spells out this restriction explicitly, it can be inferred that this right to travel to other member states does not apply to non-Schengen member states (either as destinations or as blue card issuer). As of writing this, Bulgaria is not a “Member State applying the Schengen acquis in full”. (“in full” means a member state that is part of the Schengen area, Bulgaria already applies part of the acquis, because it has to issue visas and performs border check to the Schengen standard but, as you probably know, it is not actually part of the border-free area.)