The Mega Man & Bass series, or Rockman & Forte series, is a minor sub-series within the Classic era. It consists of two games - Mega Man & Bass and Rockman & Forte: Challengers from the Future, both of which were originally exclusive to Japan, though a port of the former has since been released internationally.
Both games in the series are traditional action platformers with a format very similar to the numbered Classic series entries. Their main distinction is the addition of Bass, Mega Man's rival, as a second playable character, with his own abilities, upgrades and (to an extent) story relevance. On the timeline, both games take place after Mega Man 8[1] and presumably before Mega Man 9.
Literally "Mega Man & Bass: Challenger from the Future", Japan only
References
↑As evidenced by the Data Base in Mega Man & Bass containing robots from all games up to and including 8, as well as the appearance of Astro Man and Tengu Man.