Taking your bike on the Worcester bus.  

https://www.therta.com/faqs/bike-racks/

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Taking your bike on the commuter train to Boston

https://www.mbta.com/bikes

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Bike locker storage at Union Station

Contact the Worcester Redevelopment Authority.  There are bike lockers at Union Station - if they tell you they don't know about them, don't give up.  You may have to keep calling or emailing to get someone to respond.   The cost is/was $1/year.   https://www.worcesterma.gov/development/wra

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Complete Streets - thanks to WalkBike Worcester for helping to get this implemented.