I've just been through this experience and suggest you still have plenty of time left this year (if you get on with it now and don't delay).
I tried putting a new BB above the old hive and waiting for the bees to move up and draw the foundation...but they showed no interest and never did.
So, with the year moving on rapidly i took the following 'shook swarm' type approach which worked well and resulted after 4 weeks with 4 - 5 frames of brood in a 14x12 and 2 supers being still being filled with Honey.
1. Make sure you have a new BB, full of new frames/foundation, floor, roof, etc
2. Get suited up and make sure you are fully protected, the chances of the bees being agressive are very high.
3. Make sure there are no familly/neighbours near by, the chances of the bees being agressive are very high. Warn neighbours to stay indoors for a while if your hive is in back garden.
4. Find a couple of large clean plastic buckets and a sharp kitchen knife (a serated bread knife works well).
5. Smoke hive and wait 5 mins
6. Move old hive a few yards and place the new floor/BB on the original site. remove 5 frames from the new BB for now.
7. Remove the roof off the old hive
8. Smoke old hive again
9. Using the kitchen knife carefully and gently cut out the old comb. Work methodically and cut the comb out in managable chunks. I found that it wasn't too difficult to cut the 'plates' of wild comb out, one by one.
10. As you cut each lump of old comb out hold it above the new BB (above the space where you removed the 5 frames) and shake all bees off into new BB. Inspect each comb and make sure queen is not on it, then put in one of the plastic buckets.
11. Repeat until all old comb is removed from old BB
12. Now shake off any bees from inside the old BB, into new BB. Make sure the queen isn't in the old BB.
13. Put 5 frames back into new BB and put roof on and leave alone.
14. Destroy old BB and dispose of all old comb (melt for wax if viable?)
15. Wait 2 weeks and inspect, you should see drawn comb and eggs, if seen all is ok...if no eggs seen, add a test frame of brood/eggs from another hive.
16. If a test frame was added, Inspect 9- 10 days later and look for sealed QCs on test frame, if no QC seen then it is likely there is a queen in hive. If QCs seen, remove all but one and then wait 3 - 4 weeks for queen to emerge/mate/lay
What happened to me, was I moved the wild hive into a new 14x12 BB (FWIW I never saw a queen whilst shaking the bees off) and I inspected after a week and saw no eggs, I thought that meant no queen. So, I added a test frame of eggs/brood. On the next inspection, no QCs but there were some eggs on other frames, must be a queen there, but none found. Following inspection saw 4 - 5 frames of eggs and brood and massive expansion in a very short space of time. I found the queen and marked her - although you can easily spot her without any marking as she's huge!