The easiest answer is to just republish a refreshed data source to Online whenever you need to. Just don't create a refresh schedule on Online and you'll be ok.
You can do this programmatically too, but it's a little clunky. Bridge is an OK solution (and really, it's just Tableau Desktop, so if Desktop is already allowed on the network and can publish data sources to Online, then the only thing Bridge adds is automation. It's just as secure as Desktop.)
So unless you want to start using the Tableau API's to automate the refresh outside of Bridge, manually republishing the data source is your best bet.
I created a batch file to refresh files , which is working fine, Desktop is installed on my work laptop so right now I was able to do refresh from laptop. When I try to Install tableau desktop without activating License on a server to use command line (Tableau.exe) I got an error saying product is not activated. I hope I can't use the same license on my laptop and server to activate. At least now I have a way to refresh sources.
You should be fine using the same license on your laptop and on Server for the Tableau Desktop installation. Tableau allows 2 activations of Desktop precisely for that reason.
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That was really fast , Thanks for clarifying this. I will activate license on server and establish refresh jobs from server as scripts.