I don't think it has that feature, you can try submitting a feature request for it in support.atlassian.com OR ask someone to create a plugin for it . It's a good idea and I'm not sure if how many will vote for it.
A workaround I can think for now is to link your Pull Requests to a JIRA ticket and log the hours there.
Bitbucket Pipelines helps me manage and automate a number of serverless deployments to AWS Lambda and this is how I do it. I'm building Node.js Lambda functions using node-lambda ...
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