1 Mordekai: So Alvissa, you’re a bard, right?
1 Alvissa: Yes.
2 Mordekai: So how come we never see you flirting with random strangers, hitting on everyone in a tavern, and seducing anything that moves?
3 Alvissa: How gauche!
4 Lambert: Alvissa dates from a time before bards were sexy.

Back in the day (i.e. the 1970s and 80s era of early editions of Dungeons & Dragons) bards were seen as a bit of a joke character class. Wandering minstrels were fantasy staples, but hardly the stuff of heroic adventure, so the bard class was kind of tacked on as an afterthought. The Advanced Dungeons & Dragons rules insisted that to even become a bard you first had to gain levels as both a fighter and a thief, in order to give you some actually useful skills before you dedicated the rest of your adventuring career to strumming a lute in anger.

More recent editions of the game decided to make the Charisma stat more useful than its first edition dump stat uselessness, turning it into a kind of super personality/persuasion power. Bards were the natural beneficiaries, and they evolved into often being the party "face" - the person who talks to strangers, be they hostile or friendly, in order to persuade them to treat the party generously (or at least less aggressively).

From the power to persuade people it wasn't far to the trope of the Horny Bard. This is a bard with a James-Bond-esque penchant for romantic dalliance. Usually the horny bard has the looks and brazenness to be very successful at this, but occasionally there is the Casanova wannabe type. This idea of bards perpetually being on the lookout for their next bedroom conquest has been promulgated and popularised by various modern-day gaming vlogs and podcasts, such as Critical Role.

So while you may be familiar with the idea that bards are all like this, and think of it as natural, it most definitely was not always this way.