I'd be happy for you to make the appropriate updates, noting that cycles appear to be allowed in a westerly direction only.

Good question. Arguably there is an ambiguity in the OSM Wiki defiition of a 'bus_guideway'. The purpose-built route that is for the exclusive use of guided buses starts at the junction with Cumberland Road. The stretch to the bridge is not a conventional bus-lane (see the No-entry signs). How else should we tag it?