How can I get write access for a deployment key on Bitbucket or something like that?

All write access to Bitbucket repositories is managed based on Bitbucket users. So if you don't want to give your normal Bitbucket users write access, then you need to create an additional Bitbucket user.

Since Bitbucket bill you by the number of users I don't see anything wrong in doing this — infact, it's in their interest that you create several users.

I met the same issue, I've found related issue in bitbucket public issue tracker. https://bitbucket.org/site/master/issues/6887/additional-read-write-key-per-repository

One of the comments:

I am afraid we are not going to do this. This would mess up the way we do billing on the site. We could a user as someone with write access to a repository. There are ways around this, setting up another account with that key and only giving that user access to the repos you require.