Update 10/15/16: Unfortunately Airbnb has been pulled from MileagePlus X, so it's currently not possible to earn additional bonus points using the method outlined below.
There have been limited opportunities to earn bonus miles or points on Airbnb purchases — only certain cards like the Chase Sapphire Reserve or the Citi Premier® Card, which offer 3x points on travel purchases, would earn you a bonus. However, the MileagePlus X app from United has added Airbnb as a merchant, so you can now earn at least 3x United miles for Airbnb purchases, in addition to the points or miles you'll earn with your card.
For every dollar you spend on Airbnb, you will get 3 United miles, which TPG values at 1.5 cents each. You'll earn points from your credit card purchase as well. If you were to use the Chase Sapphire Reserve, for example, you could potentially earn 3x Ultimate Reward points, assuming Airbnb purchases through the app code as travel. So, a $500 purchase could lead to 3,000 points in total — not bad! You'll essentially be purchasing an Airbnb gift card through United's app, which you can then credit to your Airbnb account.
Further, United MileagePlus Explorer cardholders get a 25% bonus on any earnings through the app — even if you don’t use that card to make the purchase, boosting your bonus to 3.75 miles per dollar. If you don’t have the United MileagePlus Explorer Card already, you can earn 30,000 bonus United miles after spending $1,000 on purchases in the first three months if you sign up now.
Additionally, in unrelated Airbnb news, the company has begun a partnership with Qantas Airlines, where you can earn Qantas miles by booking Airbnb stays through the carrier's website. For every dollar spent with Airbnb, you'll receive one Qantas mile. Unfortunately it isn't possible to stack these promos, so purchase through United's app if that works for you.
