Of course the faster you go the slower time passes but you have to travel at least 30% the speed of light to make a dramatic difference. See the table here:
Also: the star with the shortest known period orbiting our central black hole travels no faster than 1% the speed of light.
Re:The structure of the Milky Way
by mikhailfranco on Wednesday August 01, 2018 @02:46AM
(#17660202)
Peak stellar speed observed as "nearly 3% the speed of light":
https://www.nature.com/articles/d41586-018-05825-3
which appears to be rounded up from actual 2.55% value:
https://en.wikipedia.org/wiki/S2_(star)#May_2018_pericentre_...
While reading this article and viewing the diagram of the Milky Way, I wondered, does time pass more slowly from the point of view of those bodies near the center of the galaxy, which are moving more quickly?