Here’s what I do. I have the old color on the needle. Drop that, knit a stitch with A, drop that. Purl a stitch with B, put the yarn to the back and drop it.
Now knit the next A stitch with the main strand AND tail of A. It will make a double loop this time, but you’ll knit it as one next time and you won’t notice.
Drop A, bring B and it’s tail forward, and purl the next stitch with both, and bring the yarn to the back.
When you get around to the beginning of the round, put your two colors under the strand hanging down the back before you use them again. This will help secure that and twist it. You can even twist it a few times and give it a tug to tighten up the last stitch you made with it.