Remember you are not using the TBB (browser) method for connecting to bridges in Whonix.
You need to instead manually edit your torrc file in the Whonix Gateway using either nano in a terminal, or if using a GUI, select the torrc settings option under 'Start Menu'.
So, follow the steps below to get your bridges, apply changes in torrc file and reload Tor so it will use the bridges:
I assume you are running non-Qubes Whonix. In your case if you already have the bridge references, then simply edit /etc/tor/torrc as follows:
If you are using a graphical Whonix-Gateway, complete the following steps:
Start Menu -> Applications -> Settings -> /etc/tor/torrc
If you are using a terminal-only Whonix-Gateway, complete the following steps:
sudo nano /etc/tor/torrc
Once inside /etc/tor/torrc, scoll all the way to the bottom, and copy-paste the following text:
ClientTransportPlugin obfs2,obfs3 exec /usr/bin/obfsproxy managed
ClientTransportPlugin obfs4 exec /usr/bin/obfs4proxy managed
Now you must add IP addresses for your bridges. For finding IP addresses, See section above, titled Finding a bridge and choosing the right protocol.
Copy-paste the IP addresses at the bottom of /etc/tor/torrc. Make sure to manually add the text "bridge" at the beginning of each line entry.
Example of text to add to /etc/tor/torrc. (Note: do not copy-paste this list; these IP's will not work.) (Use either obfs3 or obfs4. Not both at the same time.) Get your own obfs3 bridges or better obfs4 bridges from Tor:
bridge obfs3 184.108.40.206:22321 4352e58420e68f5e40bf7c74faddccd9d1349413
bridge obfs3 220.127.116.11:38123 4352e58420e68f5e40bf7c74faddccd9d1349413
bridge obfs3 18.104.22.1683:62389 4352e58420e68f5e40bf7c74faddccd9d1349413
bridge obfs4 22.214.171.124:42086 0EEB10BF4B4FAF56D46E cert=oue8sYYw5wi4n3mf2WDOg iat-mode=0
bridge obfs4 126.96.36.199:43263 DD21A551767816A0C9495 cert=7qzS6KASquPvJU82Fm7qoJw iat-mode=0
bridge obfs4 188.8.131.52:10703 B3B8009D01BB7E5FDFAEC cert=4RaIqGiOytEXm6Hw iat-mode=0
Once you have completed editing /etc/tor/torrc, now save and exit.
--> press Y -->
Follow steps 3 & 4 in the link to check Tor is working correctly and to apply the changes i.e. reload Tor.
Note: obfs4 is the preferred option right now. Also, only 3% of the Tor population uses bridges and these are often blocked aggressively by censors.
If that happens to you, then manually using meek, scramblesuit, FTE or other methods may be required, although this is not recommended by Whonix for various reasons. Again, this would require manual settings to your torrc file - see Tor Project docs and quickstart guides for details.