The history of the 308 and 331 are intertwined. The 308 is the older route with the 331 being formed from the 308 in 1969. No reason why the route should have a cta connection when it a major north/south connector in the inner suburbs as are the 330 and 332.
308 - Medical Center - was West Towns route #8. Bus route was introduced by Speedway Auto Bus 9/9/21 and included service north of Hines Medical Center (Speedway Hospital) via 5th Ave to Lake St. From 6/22 service extended to Hillside via Lake,19th, Butterfield, Hillside & Harrison but was withdrawn 5/16/23. Speedway sold to West Towns 7/1/30. In 1969 5th Ave segment transferred to new route #6, now Pace #331.
331 - Cumberland-5th Ave. - was part of West Towns #8 operated between Lake St and Hines VA Hospital via 5th Ave. In late 1960’s became separate #6 and extended north to Triton College in River Grove. From 5/24/76, route was extended and renumbered, basically creating present Pace route #331. That route operated north to the Park Ridge train station until 2/27/83, when the CTA rapid transit extension was opened, serving Cumberland Ave. On that date, route #290 replaced route #331 between the Cumberland station and Park Ridge. By 2000 operating from Cumberland Blue line via Cumberland, Grand, Triton College, 5th, Hines, C, Loyola, 1st, 31st to loop Maple, Ogden, Prairie, Washington & Maple in Brookfield. From 1/2/2004 rerouted between Hines & Loyola via Roosevelt and 1st. From 8/12/2019 service south of 1st Ave/31st St split into two branches M-F daytime. One branch to Brookfield Village Hall via 31st, Maple, Grand & Brookfield and the other to La Grange Metra via Ridgewood, Washington & La Grange partially replacing 304. M-F day & eve, S day.