Justin Bieber dropped by Storyville, the nightclub on Exeter Street, late Wednesday after the second of his two sold-out shows at TD Garden. Invited by promoter Ace Gershfield of 6one7 Productions, the “Sorry’’ singer made no attempt to be anonymous, hopping on the bar to dance. (The crowd, as you might expect, cheered madly.) Smoking a cigarette and wearing a black T-shirt revealing his heavily tattooed (if somewhat scrawny) arms, the 22-year-old Canadian pop star grinned as he danced, a wedge of lime in his mouth like a mouth guard. We’re told Bieber asked DJ Dolo to spin Justin Timberlake’s “My Love’’ and “Senorita,’’ and then climbed up onto the bar. The singer stayed at the Four Seasons Hotel while in town and was spotted in the Boston Public Garden, once wandering in bare feet and once sitting in a tree listening to music on his headphones. If this is “bizarre’’ behavior, as some have said, then Henry David Thoreau was completely nuts. Bieber also played pool at Jillian’s and stopped by Nick Varano’s STRIP by Strega.