Unless it actually managed to pierce your artery, no. Even if it did, then binding your arm above the wound tightly would stem the flow of blood. Given that Beedrill's stings are capable of poisoning pokemon, however, it's probably better to remove it.

*he's keeping his own tone calm and level, though he'll add just a hint of authority if he needs to get the point across*

Just have some cloth or bandages prepared in advance, then go one step at a time. If it starts bleeding heavily, then wrap one tightly around your arm above it first, then go on to do the other steps.