Collins Russian Dictionary 2nd Edition © HarperCollins Publishers 2000, 1997:
blissfully [ˈblɪsfəlɪ] adv блаже́нно
blissfully happy бесконе́чно счастли́вый
blissfully unaware of ... в счастли́вом неве́дении о +prp ...
* is used to mark translations which have irregular inflections. The Russian-English side of the dictionary gives inflectional information.