What was Big Willy Shakes going for?
Of course, the joke's not just on Bottom. It's on Titania too because she's been charmed with Oberon's love juice. She literally fell in love with an "ass." Yes, Shakespeare is making an allusion to bestiality, even though Bottom remains human from the neck down.
More importantly, Shakespeare is also making an allusion to another kind of sexual relationship that was considered completely inappropriate: a relationship between a commoner and a royal, which would have been viewed as "monstrous." (This was a big no-no in Shakespeare's day.)
Bottom tries to tell the "the short and the long" or the plain truth about what is happening, but the truth is, he's unable to because he just doesn't have all the facts. You probably noticed how we, the audience, have a lot more information about what's happening on stage than the characters do.
Case in point: throughout the play, we know the fairies use magic to play pranks, but the humans have no idea what's happened to them. Bottom is magically transformed into a donkey but he has no clue. Titania is given a love juice but she doesn't know it.
This is a classic case of dramatic irony, when the audience knows more than the characters do. It also means that the characters' words and actions have a different meaning for us than they do for the characters on stage. It's a technique Shakespeare uses all over the place for comedic effects throughout A Midsummer Night's Dream.
It's used so much, in fact, that even this very statement becomes dramatic irony. There is no truth about what's happened anymore because even the characters don't really know what took place. So when Bottom says something is the "short and long" of it, we know there's no long of it, and there's no short of it. Only the audience knows for sure what happened to Bottom and Titania.
It turns out Shakespeare was fond of this little phrase he coined. A few years later he used it again in The Merry Wives of Windsor. This time, it became "the short and the long of it."