Car sharing is one option, which is already proving popular in other parts of the country. York's own car share website - www.carshareyork.com - matches drivers and passengers for both daily and one-off journeys.
Users can log onto the free website and register where and when they are travelling. The site then provides a match for anyone who is already making that journey. Anyone wanting more information should visit the website or call 08700 111199.
Residents can also take advantage of over 100km of cycle tracks in the city. The York Cycle Route Map is available free of charge from cycle retailers, libraries, council receptions, or by visiting www.york.gov.uk/outabout
Andy Hudson, assistant director, environment and development, said: "First have assured us that they will continue to run Park & Ride services from Rawcliffe Bar, Askham Bar and Grimston Bar, though at this stage they cannot confirm that services from the McArthurglen designer outlet will run.
"The council is doing all we can to minimise congestion and disruption and one of the key ways residents can help is by using alternative forms of transport such as walking and cycling and by putting off unnecessary car trips where possible."
The council's transport planning team will release information about alternative bus routes for cancelled services in the next few days.