Our club (South Herts CTC) had to cross the A505 to get back into Hertfordshire on Sunday and we took a route between Litlington and Therfield which involved 500 m along the A505 and a right turn at the roundabout west of Royston.
I was quite surprised there was no cycle route to help cyclists here. It was a Sunday so at least there were fewer heavy vehicles than normal, but the speed of some cars coming up behind made it tricky to change lanes on a bike when turning right at the roundabout.
Since then I have studied other ways of crossing the A505 (using Google Streetview) and can't find any easy crossing points near Royston. I see it is the boundary between Hertfordshire and Cambridgeshire, which complicates matters (although it looks like the A505 road is in Herts).
To the east, I've used the B1368 crossing at Flint Cross, which is also a nightmare. To the west the crossing at Slip End does at least have a central refuge. It seems little or no thought was given to cyclists when the A505 was constructed.