I'm a bit surprised you bother with a travelling steady – I've used one maybe half-a-dozen times in 40+ years, and only for turning lengths of about 10 diameters or more.
Your total depth of cut only needs to be 0,25mm or about 10 thou, and you've only a length of 6 or 7 diameters to turn. 3-jaw chuck plus tailstock running centre should do fine. I'd probably do 2 passes of about 0,2 and 0,05mm, but that's only if the 12mm diameter has a tight tolerance.