I think there is a sneaky user preference that may help in this situation - ‘Consider topics unread when they are closed’. You can find it on your https://meta.discourse.org/my/preferences/tracking page.
If you uncheck that it stops a topic close from being counted as ‘unread’.
ETA: Though there doesn’t appear to be an admin setting to choose the default in the same way as a lot of the other user preferences (the ones in /admin/site_settings/category/user_preferences). That might be a nice addition.
And just to clarify, when you say ‘bumped’ do you mean that they get the blue unread indicator and appear in /unread? I don’t think closed topics are bumped in the traditional way where they get put at the top of /latest (whether manually closed or by a timer).
Also, I think the auto-close timers use a ‘silent’ version of closing already where it suppresses the unread indicators, so hopefully those ones are not appearing in /unread lists. 