I have just completed my first multiplayer game in the new expansion where you receive XP for doing different things.
I got 25% bonus XP for playing with friends, are there other things I can do to get bonus XP like this?
This feature isn't fully implemented just yet, so there aren't much ways to get bonus experience at the moment.
Blizzard has stated the following in an interview with PC Gamer (prior to game release):
We’re already working on concepts like “bonus XP for your first win of the day” and “extra XP when you play in a party with a Battletag or Real-ID friend”
We’re considering “bonus XP weekends” and other sorts of activities, which will be tested in the beta.
Aside from playing with a friend and first win of the day, it doesn't seem that there is other ways to get bonus experience as of right now.
It seems that the first win of the day bonus can be awarded for every race.