We transitioned when DS was about the same age as yours (but not in 1-0 at all!), purely because of a holiday we were going on. He'd also been in a sleeping bag and was very excited about the prospect of a BBB! We chose the duvet cover/pillow set together online and he was so excited when it arrived! We just about managed to set up the BBB and cot in his room together, with perhaps a mm to spare, but it worked
He hadn't used a pillow until this time, and since the pillow arrived before the mattress, I decided to let him try it at nap time, in his cot. He was so incredibly excited about his Mickey Mouse pillow that I feared he wouldn't be able to sleep at all, so I said "don't worry, if you find it too exciting and just can't sleep, I'll take it away and you can sleep without it, as you're used to". Well of course I could just hear him playing around at nap time so after half an hour or something I went in and told him I'd take it away if it was keeping him awake. Well he just carried on so I had to keep my word and he was so upset, I can't remember if he actually napped at all in the end, but the next time, there was no messing around at all, straight to sleep
So when the mattress arrived and I set up his bed and he was incredibly excited again, I told him "don't worry, if you find it too exciting and just can't sleep in your BBB, you can always sleep in your cot and try again tomorrow" - after the pillow incident, he knew I was serious and there was no messing around at all, I don't think the idea of getting out of his bed even occurred to him as he still had the monitor and was used to getting our attention that way, in fact he continued to use that rather than getting out of bed until DD was born and she got the monitor
I can't honestly remember whether he just did naps in his BBB at first, and then nights once he was used to it for naps, but the cot stayed up in his room for a while and once he was in the BBB he certainly didn't want to go back into the cot, so there was no messing around at all! I should add that we had a guard rail, which certainly helped keep the covers on as well as stopping him from falling out.