On this specific issue, I'm opposed to self-signed certificates, especially over commercial products like Atlassian Stash. Your company has purchased Atlassian Stash. You'll be much better served by also purchasing and installing an SSL certificate for the server, rather than fighting with self-signed certificates.
Yes, it is possible in some cases to make self-signed certificates work, but they are brittle and hard to maintain. You'll spend more maintaining self-signed certificates than the cost of the SSL certificate.