Had a look on OSM and various sources on google, however, there does not appear to be any obvious websites.
I specially want the number 52 bus route for this current task but if there is a general mechanism or website with other routes on this will be helpful in the future.
While it's not publicly noted, it would appear that all the shapefiles are available in GEOJSON format at urls with the following structure:
https://ccts.arcticapi.com/network/operators/CB/lines/<linenumber>/shapes
For instance, https://ccts.arcticapi.com/network/operators/CB/lines/9A/shapes and https://ccts.arcticapi.com/network/operators/CB/lines/4/shapes for lines 9A and 4, respectively. The specific shapefile for the #52 line requested is located here
This is a good example of data that is effectively public but not explicitly published, and a formal request to include it in https://foi.cardiff.gov.uk/eng/Pages/OpenData_All.aspx or another appropriate public open data portal may be prudent.
