Raducanu followed up her maiden WTA Tour win over Polona Hercog -- a battling three-set victory on Tuesday -- with a much improved performance against Bogdan and looked steady on serve, winning 87.5% of her first serve points.
"It was so good to play a Romanian here. All the volunteers who go into making this tournament possible, we really appreciate their support. Ana was a great opponent," Raducanu said after the match.
"It's definitely taking me some time to find my feet still. I'm taking some learnings from every match I play. I still don't think I'm the finished product yet."
Raducanu, who announced herself on the grandest stage when she claimed the Flushing Meadows title as a qualifier last month, added that she has gifted her U.S. Open trophy to the Lawn Tennis Association (LTA).
"I just thought the LTA had done so much for me and I just wanted them to have it as a sign for everything they had done for me. It's a little gift," the British No. 1 said.
Raducanu will next face 19-year-old Ukrainian Marta Kostyuk.