Sam Vesty scored 20 points as the Aviva Premiership outfit strolled to a five-try victory at Arcul de Triumf.
The 2008 winners had not won on the continent in European competition for five matches since their triumph against Aironi in the Heineken Cup.
Lock Will Spencer and hooker Ross Batty scored first-half tries before Vesty, Ollie Devoto and Kane Palma-Newport all crossed to seal maximum points for Gary Gold's troops.
Bucharest scored twice themselves through Florin Surugiu and Christian Munteanu, but Bath have applied pressure on their group rivals Calvisano and Agen, who face each other in the late kick-off on Saturday.
Meanwhile, London Welsh were heavily beaten after facing a tough baptism of fire in Europe against established French outfit Stade Francais, who claimed a comfortable 68-19 nine-try win at the Kassam Stadium.
Outside half Gavin Henson scored the first points for the Exiles at this level, but Lyn Jones' men trailed 35-16 at half-time.
Stade Francais hooker Remi Bonfils and centre Waisea Vuidarvuwalu both crossed twice to secure the bonus point before Hugo Bonneval touched down for a fifth first-half try.
Daniel George scored Welsh's first try, but Felipe Contepomi added the gloss on an excellent individual display with a 75th-minute score in a 25-point haul as Stade started their Pool Five campaign in style.
Welsh face an uphill battle in this pool after Grenoble hammered Italians I Cavalieri Prato 59-3 on Friday night.
Worcester Warriors taught Gernika a severe lesson with a thumping 85-5 success in Pool Two.
This was the Spanish champions' European debut, but it turned into a nightmare as the Warriors crossed 13 times.
Gernika wing Toto Mazzochi scored on the hour mark, but the joy was short-lived as Richard Hill's side ran riot in this one-way contest.
Replacement Max Stelling grabbed a six-minute hat-trick late on, wing Andy Short and scrum-half Paul Hodgson scored try doubles while number 10 Joe Carlisle bagged 25 points with a try and 10 conversions.
Yet the challenge in weeks ahead will be tougher for Worcester, who take on Perpignan next weekend.
The French giants thrashed Rovigo in a 10 try 79-12 romp at the Stadio Mario Battaglini this afternoon.
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