At first I thought this might not be possible, but then I have looked into this in more details on my test environment, and I have found that bbPress assigns a custom field named '_bbp_forum_id' to each topic and reply.
This means, that a custom field filter can be used to filter the topics and replies by forums. Please follow the steps below to create such a filter.
1. First you will have to get the IDs of the forums. To do that, click on the 'edit' button under the Forums menu. The forum editor will open, and in the browsers URL bar, you will be able to see the forum ID. Take a note of all the forum names and the IDs, you will need them.
2. Now, under the Frontend Search Settings -> Custom fields panel you will have to create a new custom field based filter. If you need more information about custom field filters, check this documentation first.
3. Now, in my case the forum IDs were 406 and 411, so I have made the following filter: https://i.imgur.com/Ns8u55v.png
This is where the forum IDs and the names were needed. My drop-down values textbox contained this text:
||Choose a forum** 406||Test forum 1 411||Test forum 2
4. Also, make sure that the settings are enabled and visible. I am using this configuration: https://i.imgur.com/NwnqPIZ.png
5. This resulted in the following layout for me: https://i.imgur.com/5taEzLO.png
Basically a simple drop-down box with a forum selection.
I hope this helps!Best,
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