As far as I know, Google Analytics filters will let you include or exclude traffic coming to your site, not traffic going away.
exclude -> traffic to hostname -> exampledatabase.com will not work, except if you're using the same Google Analytics property id on both sites. Judging by your question that's not the case, they are tracking on their own property id. So,
exampledatabase.com will never show up in
example.com's Analytics data.
If you want to "tweak" Google Analytics for decreasing your bounce rate when visitors navigate from
events: They reduce bounce rate, do not inflate page views.
virtual page views: They reduce bounce rate, inflate page views.
Events: Fire an event when your visitors click an URL pointing to
databaseexample.com. Read Track outbound links.
@GeorgeAnt was on the right track, except for the value for parameter
opt_noninteraction, he said set to
true, it should be on its default value
GeorgeAnt's linked reference (same I included):
By default, the event hit sent by _trackEvent() is considered an
interaction hit, which means that it is included in bounce rate
calculations. However, when this value is set to true, the type of
event hit is not considered an interaction hit.
Track Virtual page views: Fire code when your visitors click an url pointing to Site B, and set a virtual URL, something like
You could also track traffic from both domains into one property id, maybe that's what you're looking for, here is the documentation.