After you have received accesstoken & secret, when you send the request add a (Authorization) Header as,
Authorization: OAuth oauth_consumer_key="<YourKey>",oauth_signature_method="HMAC-SHA1",oauth_timestamp="<TIMESTAMP>",oauth_nonce="2694561796",oauth_version="1.0",oauth_signature="<Signature>"
TIMESTAMP= current epoch (ms) oauth_nonce random number
Important thing is oauth_signature
Read through here on how to generate,
Signature has to be precalculated before sending the request. And this will do it.
To test it you can tryout it here, Apigee Bitbucket API Console
PS: Its weird that Bit Bucket uses OAuth 1.0, well known for its vulnerabilities.