Bitbucket don't have a published method to query an access token.
You can see all the OAUTH methods here:
OAuth on Bitbucket Cloud
It probably doesn't matter, since they expire tokens every 60 minutes, so you would most likely need to request a refresh any way. And in the refresh it will give you a new access token, and tell you the expiry again (in 60 minutes) and also the permissions (scopes) you were asking about.
A refresh response doesn't need to occur within the 60 minute limit, so you just refresh when you are about to use it. It will respond with:
{"access_token": "", "scopes": "", "expires_in": 3600, "refresh_token": "", "token_type": "bearer"}
Where permissions would be like: "wiki pullrequest project team account" and they are also listed under the linked page above (in the Scopes section).