What happens when you pick up rune, when you already have one bottled

Solution 1:

You can have only one Rune in the bottle at a time.

1. If you pickup a second rune, it activates it as if you had normally picked it up
2. If you activate your bottle rune then you can store the other one in it

What happens in the video is the scenario 1. The Bounty Hunter stores the Double Damage in the bottle then activates the illusion rune by picking it up. You can see the Double Damage still sitting in the bottle when he selects back his Hero.

Solution 2:

A bottle can only hold one rune at a time. As you suspected, if your bottle already contains a rune and you pick up another one, it will behave as if there is no bottle and instantly activate it.