Colorado Springs Airport: The sensible transfer is a rental car or rideshare: Manitou Springs is roughly 20–30 minutes west of COS, typically about $30–50 by rideshare before surge. There is no clean, direct airport-to-Manitou public-transit link; do not burn a short trip trying to stitch together airport buses and transfers.
Denver International Airport: Only use DEN if its airfare is substantially better or you are combining Manitou with Denver. Rent a car for the roughly 1½–2-hour drive in normal conditions; traffic on I-25 and winter weather can stretch that sharply. Airport shuttles to Colorado Springs are an alternative, but still leave you needing a rideshare or Mountain Metro connection west to Manitou—usually a poor trade for a weekend.
Downtown Colorado Springs / intercity bus arrivals: From downtown Colorado Springs, Mountain Metro’s Colorado Avenue service (Route 3) is the useful local-bus corridor toward Manitou; allow roughly 30–45 minutes depending on the stop and traffic. A rideshare takes about 15–20 minutes. Check the current timetable and fare: local service is workable, but not frequent enough to treat as a turn-up-and-go metro.