The University part-funds the Universal bus service, which links Churchill with West Cambridge, the railway station, the Cambridge Biomedical Campus (including Addenbrookes), and many other University sites (such as Sidgwick). The stop nearest to Churchill is on Madingley Road, just a little further down from the pedestrian crossing which leads towards the maths faculty.
Current members of the University can travel for a discounted fare of, currently, £1 per journey on the presentation of their valid University Card.
Please note however, that these services may be impacted by the coronavirus pandemic.
Details of the route and timetable can be found at https://www.environment.admin.cam.ac.uk/travel/catch-bus and on Twitter at @busuniversal where you can get live updates and information on the free My Bus Trip App.