I think you're comparing apples to oranges. As far as I know BitBucket doesn't offer a self hosted solution but GitLab offers both. In fact they match BitBucket

I think you're comparing apples to oranges. As far as I know BitBucket doesn't offer a self hosted solution but GitLab offers both. In fact they match BitBucket on pricing too, well at least for the free tier. You can host private repos directly on GitLab and BitBucket for free. The self hosted option may not be right for you especially if you're already using BitBucket private repos. Why did you not try GitLab's hosted private repos?