When I saw that first time, I hadn't realised where it was. I've crossed that a few times.
I would enter on the right hand lane, as you would in a car, then, once past the Bilton exit, signal left and look to change lanes. Someone let's you in, or there's a gap, but I take the lane until I can move over.
If you like a challenge, have a bash at the Dunswell Roundabout. I'm not sure how to link maps, so I hope this works.
https://www.google.co.uk/maps/@53.7949958,-0.3691627,277m/data=!3m1!1e3
Entering from the south and heading east is tremendous fun! You need to stay out to be visible to those entering from the north, but you're then faced with people using the inside lane, while others grow impatient behind you.
Even going straight across, the lane you need doesn't exist until you're almost on the roundabout, so you have to take the other lane very early, then hold a lane on the roundabout while the cars on it are trying to shift lanes at 40mph+.
There is a cycle path on the east side of the roundabout, but where it joins the road, you can't actually see if anything's coming from the east, generally at 40mph+in order to cross the carrigeway.
It takes assertiveness to a whole new level.
EDIT
I forgot to say, all the above relies on being on a roadbike. Trying it on my mountain bike's a whole different challenge. I've no idea how they expect the bulk of cycle users to attempt that.
I think, once a road layout is changed or created, the designer should ride it several times in differing conditions, and produce a video of how they expect cyclists to use it, and pointing them at the cycle lanes is a secondary option.