Github has actually been working on a git extension for large data files. They support it on their system, as well as on Gitlab. I don't know about whether Bitbucket supports it though.
You can find the git large file support extension here: https://github.com/github/git-lfs
I'm not 100% convinced to the benefit of this. Its not like a diff or a merge can be done effectively between large binary files (I know perforce can do it between images but its rarely useful). Our artists often put the raw data (i.e photoshop sources) on a versioned rsync server instead. Only the output assets (i.e png files) and code should really be on a version control.
rsync is faster and more scalable than any version control can be I suppose.