You might need to contact Tableau support for this information.
Alternatively, you can probably figure it out yourself if you install a tool like Fiddlr on the server and trace the network activity.
Thanks Tom, I have a case raised with Tableau. Initial response from Tableau was to open the port 443 and 80 however they have not mentioned about the range of IP address needs to allow. Waiting for Tableau's response.
I know you got this working a long time ago, but here's the answer for posterity:
Bridge does not require any INBOUND port connections to work. It does require outbound connections on port 80 and 443.
If you wish you can restrict the outbound connections to the IP address ranges for specific pods:
Tableau Online: Keep Data Fresh (Best to reference the help article, it will always be up to date - not that we change IP ranges but we add pods sometimes).