I want to configure my Tor Browsers to use a private Bridge but cannot locate any documentation which gives the specifics.
I think this is the documentation that you are looking for:
Understanding A Bridge Configuration Line
As an example, when you obtain a bridge from https://bridges.torproject.org, you'll get a bridge entry that looks like the following:
- 18.104.22.168:443 4352e58420e68f5e40bf7c74faddccd9d1349413
Understanding the components of a bridge line isn't strictly required but may prove useful. You can skip this section if you'd like.
The first element is the IP address of the bridge: '22.214.171.124'
The second element is the port number: '443'
The third element, the fingerprint (unique identifier of the bridge), is optional: '4352e58420e68f5e40bf7c74faddccd9d1349413'
Now you need to edit it as you need.
How to add this line in TBB is written here: