A user is considered as a bounced user when he/she lands on site and doesn’t do any other activity apart from the first activity, which is basically a pageview. User becomes active and bounce rate changes as soon as he performs any other activity on site which is being tracked by GA. For example, if a user navigates to another page or triggers an event.
Two things could be causing the bounce rate to fall after you implement GTM; one good and one bad.
When you implemented GTM, you did not remove the old GA code that was added to your site directly. This would result in double counting of each pageview reducing your bounce rate. This can be fixed by removing the GA code.
There are some events that are triggered without a user doing an action. For example:
When a popup loads.
When an item comes into view.
Tracking visit to specific pages.
Recording banner impressions on landing pages etc.
For these event tags, Google Analytics allow setting them to Non-Interaction (not have an effect on the bounce rate of site).