Actually, I think you may be seeing a different problem. Can you open up your JavaScript console via "Inspect Element"? I seem to be seeing an Internal Server Error when "Import" is clicked.
Logs show:
Started GET "/import/bitbucket" for 127.0.0.1 at 2015-08-10 12:02:46 -0700Processing by ProjectsController#show as HTML Parameters: {"namespace_id"=>"import", "id"=>"bitbucket"} User Load (1.4ms) SELECT "users".* FROM "users" WHERE "users"."id" = 1 ORDER BY "users"."created_at" DESC, "users"."id" DESC LIMIT 1 (0.8ms) BEGIN (0.7ms) ROLLBACK ApplicationSetting Load (0.9ms) SELECT "application_settings".* FROM "application_settings" ORDER BY "application_settings"."id" DESC LIMIT 1 Namespace Load (1.1ms) SELECT "namespaces".* FROM "namespaces" WHERE "namespaces"."path" = 'import' ORDER BY "namespaces"."created_at" DESC, "namespaces"."id" DESC LIMIT 1 Rendered public/404.html (0.7ms)Filter chain halted as :project rendered or redirectedCompleted 404 Not Found in 51ms (Views: 34.5ms | ActiveRecord: 5.8ms)
My guess is that your access_token and access_token_secret have expired, but they are stored in the database and are never ever cleared out. If you are running your own instance of GitLab, you can manually clear them out as a temporary workaround. !1112 (merged) was supposed to address this, but it needs some work.
I don't see this as token expiring problem, because I authorized gitlab website to access my bitbutcket account and shortly after that used the import function. All in span of ~2 minutes. Also, I'm just using your free hosting on gitlab.com, I'm not using your self-hosting solution. If this is not the problem of your self hosting solution and this is not appropriate place for reporting website bug, please tell me the appropriate place and I will report issue over there.