Here's my theory.
He picked up an empty suitcase from the lock-up in the morning.
He drove after picking up Bee to a quiet place in Gunthorpe. There's a grass verge here for instance which is quite secluded.
Google Maps
He's put his arm around Bee as if to pull her over for a hug, and strangled her. Then pushed her down into the footwell and thrown a coat over her, or a blanket or something.
Then he's got out of the car and paced up and down the road having a *advertiser censored* (detail in his story), always keeping the car in his sight. Perhaps it was deliberate that he would get out of the car as if to be seen looking for her. Then he's got to get her in the suitcase so he turns his phone off and drives out to a remote spot in the countryside, a quiet lane with a verge, about 30-40 mins away, which is also when he uses the daylight to scope out a place for the disposal/burial. He then puts her in the suitcase and returns to the area he was supposed to be looking for her, and turns his phone back on to call SaW. Then he comes up with the idea that they were going to go to McDonalds and that's why he rushes off there, to explain the delay of 2 hours after picking her up. They later realise he won't be able to use that as an alibi as he only bought food for himself (Bee didn't want one is in his story). It's Glinton McD's to explain another part of the delay that morning.
Then he's gone back to the lock-up and put the suitcase in, 10 mins there before he goes back home.
That night they visit the lock-up together for 20 minutes, for SaW to see her for a last time.
He returns the following morning at 2:47am for 10 minutes. Searching for a shovel, but SaW wants to be at the burial so he leaves the suitcase in situ. Perhaps getting also the dimensions of the suitcase. He goes off for 2 hrs 17 mins, so if he's got to dig in that time it's probably only an hour of that driving, half hour each way. Also matches with the distance gone the day before. He prepares the hole in the ground and covers it over with branches. Back to the lock-up for 23 mins at 5:37am. Probably wet and muddy, he needs to clean himself up before he goes for another McDs.
They return to the lock-up for 5 minutes after midnight on 20th to pick up the suitcase and take it to the burial spot after Cowbit and Glinton when they have their phones switched off.