Is there a way to check how many consecutive days I've gotten the Daily Bonus?

No.

On Android version 0.45.0 and iOS version 1.15.0, there is no other way to check your progress than spinning the first pokestop of the day, or catching the first pokemon of the day.

Starting from today (26th of March 2020, version 0.171.0 on Android), you can see where you are in your streak, and if you did it for today. A filled golden circle means you have done it, an open golden circle indicates that you still need to do it, to continue your streak!