Mega Man forces the approach, which is always an advantageous trait. Bowser is more than capable of getting in on the Blue Bomber thanks to Tough Guy, his generally high movement speed, and waveslashing (if customs are on), though. From there it's mostly a matter of outspacing and outslugging him. Just keep in mind that Rock's got solid weight and some hard-hitting moves in his arsenal, so Bowser doesn't outmuscle him quite as easily as most characters.
Mega Man's Objectives
-Rack up damage on Bowser from afar and force him to approach
-Carefully play around Bowser's Tough Guy passive and defensive options to eventually get him up in the air for aerial juggles
-Knock Bowser far enough offstage to force him to use Fortress to recover, and pay attention to his timing/angling
-Finish him with Charge Shot, Mega Upper, Dsmash, or an appropriate aerial
Bowser's Objectives
-Manmode through lemons and Crash Bomber while avoiding Metal Blades to close the gap without taking too much damage
-Stay grounded unless you see a good aerial opportunity, and defend with Usmash or Fortress when appropriate
-Utilize throws, tilts, and jabs to get Mega Man far enough offstage to force out his Rush Coil.
-Pay attention to Mega Man's recovery timing/angling, and use fire breath, aerials, Dtilt, or Bowser Bomb for edgeguarding/ledge option punishing
Overall, this is a MU where both characters will have to work hard to gain the upper hand. Mega Man will have to break through Bowser's defenses, and Bowser will have to maneuver through Mega Man's weapons. To me, it's either 50-50 or 45-55 in favor of Mega Man. Either way, Tough Guy really pulls its weight in this MU, preventing it from being a clear 40-60 or worse.