Whenever I try to connect the git via eclipse mars, I entered the bitbucket URL as the instructions in this website.
http://crunchify.com/how-to-configure-bitbucket-
In my experience it seems that it happens under Windows with certain configuration of Eclipse (not sure which ones).
Go in Eclipse Preferences -> Team -> Git -> Configuration, and click "Add Entry..."
Put "http.sslVerify" as key and "false" as value (no quotes).
In the "clone repository" window put your user / password (don't leave "git", since there is no ssh-key configured under Windows, I suppose).
If needed, in the Git Repository view, check the properties of your new repository and double check that remote.origin.url has your username rather than "git" (otherwise during authentication you'll have a greyed out username textbox with "git" written in it).