You can get the Buddypress Activity Bump data on the “bp_activity_bump” key of the BuddyPress/BuddyBoss “activity” Rest API.
{ "user_id": 1, "component": "activity", "content": { "rendered": "" }, "date": "2023-04-26T07:32:13", "date_gmt": "2023-04-26T07:32:13", "id": 797, "link": "http://buddypress.local/activity/p/797/", "primary_item_id": 0, "secondary_item_id": 0, "status": "published", "title": "admin created a poll", "type": "activity_poll", "favorited": false, "user_avatar": { "full": "http://buddypress.local/wp-content/uploads/avatars/1/1663828147-bpfull.jpg", "thumb": "http://buddypress.local/wp-content/uploads/avatars/1/1663828147-bpthumb.jpg" }, "bp_activity_bump": { "activity_bump_date": "2023-04-26 05:52:41", "favorite_count": "" }, "_links": { "self": [ { "href": "http://buddypress.local/wp-json/buddypress/v1/activity/797" } ], "collection": [ { "href": "http://buddypress.local/wp-json/buddypress/v1/activity/" } ], "user": [ { "embeddable": true, "href": "http://buddypress.local/wp-json/buddypress/v1/members/1" } ] } }