I should maybe point out that I am using Ultimate Member integrated with BBpress – could that be the reason that the emails are not sending?
1. You should be aware that many spam filters strip messages that do not come from the correct address. So if your site is mysite.com and your email address in wordpress settings>general is firstname.lastname@example.org then it is likely that messages will be dumped in transit. You need to set up email to come from your site eg email@example.com, your hosting provider can help if needed.
2. Just bbpress?
Then you need to see if this is wordpress wide or just bbpress.
it could be a theme or plugin issue
As a test switch to a default theme such as twentyfifteen, and see if this fixes.
If that doesn’t work, also deactivate all plugins apart from bbpress and see if this fixes. if it does, re-enable one at a time to see which is causing the error.
If you cannot do this to your site (say because it is live) then use the ‘troubleshooting’ features of this plugin to let you test without affecting other users
Health Check & Troubleshooting
Then come back
and of course
By default, you do NOT receive emails for your own topics/replies, only if somebody else replies on your subscribed topics
so testing would need two email accounts to prove !