Use the "User Endpoint" for API 1.0
https://confluence.atlassian.com/display/BITBUCKET/user+Endpoint
The call your looking for is: https://bitbucket.org/api/1.0/user/privileges
You need to call this with user authenticated:
curl -u "USER_NAME:USER_PASSWORD" https://bitbucket.org/api/1.0/user/privileges
This will return a list of teams:
{u'teams': {u'team1': u'admin', u'team2': u'admin'}}