I'm unable to access my computer and test this myself now.
If I start a dota game up and it's a bot game, are there abandons? If I leave will I receive an abandon?
Although you are not supposed to get an abandon from a custom bot game (what I assume you are referring to), there is a common glitch that can happen to new players who have't played many pub (public) matches. This glitch results in showing bot games that are left early as abandons and will not put you in low priority but will give you more abandon percentage. There is no solution to this glitch but if are playing offline or you play more pub games then the problem will most likely solve itself at some point. However, if you are just asking if you will get abandons from leaving bot games early, then technically, no.
It depend on which kind of game :
Hope the difference between the two is clear.
If you are playing an online Co-op bot match then yes leaving will count as an abandon. However if you are playing a local offline bot game that you created of if you are playing a lobby game neither of those count as abandons.
Hope this helps! :)