Hi Sbanalla, congrats on your first edit, welcome. 

Tho dedicated bus lanes are marked differently: https://wiki.openstreetmap.org/wiki/Bus_lanes

So instead of making a separate way tagged as motorway with name bus, use lanes:psv= on ways for Oxford street

https://www.openstreetmap.org/way/612618149
https://www.openstreetmap.org/way/977069063
https://www.openstreetmap.org/way/1243077884
