Question: I'm looking for some way to block a possibility of making merge of pull requests on the BitBucket if some specified Jenkins task is currently running. Do you know if it is possible? I was looking for that in the Jenkins Git plugin and in the settings of BitBucket but with no success...
Thank you in advance for any help!

Answer: 
In bitbucket go to the project and then the repository you want to enable this feature for, and under settings->pull request check the option

> 
> Requires a minimum of [n] successful builds
> 
> 
>
This can be done using the bitbucket build status api.

1) Enable require minimum 1 successful builds in bitbucket repo settings
<https://blog.bitbucket.org/2015/11/18/introducing-the-build-status-api-for-bitbucket-cloud/>

Then either:
Manually in jenkins pipeline fire the API calls to set the build status to in in progress, failed, success

Alternatively, using something like the <https://wiki.jenkins.io/display/JENKINS/GitHub+Branch+Source+Plugin> which will do this automatically for you (sending the statuses) plus a host of other things (like automatically discovering new repos with Jenkinsfiles)