Trying to be "facts forward" so make of this what you will. Source: I was in FFA in highschool in a beef intense-ish area.

The method of collecting semen I'm most familiar with is when they take a female cow in heat and tie her up, then bring a male bull they want to collect semen from into the same pen. The male will smell the female is in heat, gets erect, and will attempt to mount her.

As the male is trying to mount the female, people in the pen with the cattle will have a large rubbery "sleeve" on a pole (imagine a cow sized condom on a stick) that they will maneuver around the bull's penis as it mounts the cow. He does his thing in the condom thinking he's inside the female (usually less than 30 seconds) dismounts and then the ranchers have their semen for artificial insemination.

I've been out of that area for over a decade now so a new method may have emerged since then, but in my Animal Sciences class, that's how we were taught semen is harvested for most livestock.

Edit: I distinctly recall the "artificial vagina" being on a stick (and laughing about it in class), but best video I can find on the quick: https://youtu.be/-4ma3WeOxbo