I got round to this just as the thermometer hit 92 yesterday.
Still, it'll keep.
This is a bit plain and there is a BIG space on the front just asking for some kind of decoration, but it's what I was asked for

Worsted weight yarn and a J hook
This is worked in the round, no seams
I know that it's usual to use stitch markers and count your rows etc, but I use the hold up and see method, so I hope you can follow this.
Also, check before you begin that your hot water bottle will fit, I started with 15 stitches because that was how big the very bottom of the bottle was.
Chain 17 (15 and 2 to count as your first hdc)
First round
hdc into second 3rd chain from hook until second last stitch on chain
2hdc into last stitch, one chain, 2hdc into the other side of the last chain (you're going back down the other side of the chain now)
2hdc into each chain until second last stitch on chain
2hdc into last stitch, one chain then one hdc into the first chain on the other side
Join to the turning 2 chains with a slip stitch
Second round
Chain 2 (this counts as your first hdc)
hdc in each stitch around to last stitch
2hdc in the chain of the previous round
hdc in each stitch until the turn again, and 2dc in the chain of previous round again.
hdc in next stitch the join with a slip stitch to your first hdc of this row.
Third round
hdc in each stitch around, don't join with a slip stitch
Fourth round
hdc in each stitch in the round.
(continue until the cozy is tall enough to reach the neck of your hot water bottle)
The cozy will be a nice envelope shape by this point, with well defined turns, so that when you lay if flat, you will be able to see where the fold falls.
This is where you make the strap
One stitch in from the fold, sc 7 stitches, chain 1 to turn
(Chain counts as your first sc)
sc 6, chain 1, turn
continue until your strap is 1/2 inch as long as you like, then make a button hole
sc1 in second stitch from hook, chain 3, 2sc, chain 1 to turn
6sc, finish off
Strap 2
Remember you are starting strap 2 on the same side of your work as you started strap 1!
Again, lay the work flat and this time count 8 stitches in
sc 7 stitches, chain 1 to turn
(Chain counts as your first sc)
sc 6, chain 1, turn
continue until your strap is 1/2 inch as long as strap 1, then make a button hole
sc1 in second stitch from hook, chain 3, 2sc, chain 1 to turn
6sc, finish off
Button
Using contrasting colour,
6sc in a magic ring, join with a slip stitch to first stitch, chain 1
Using main colour
1sc in same stitch as the first chain
2sc in each stitch around, join with slip stitch to first chain, chain 1
Using contrasting colour
1sc, 1dc all the way around, join with a slip stitch, finish off, leave a 18inch tail.
Using a yarn needle, use the tail to make a continuous slip stitch through the front loops of each stitch around.
Pull the yarn tight and it makes a wee mushroomy shape. I stuffed all the tails from changing colours inside which stuffed it enough.
Sew the button into the middle of the cozy leaving a long enough "stalk" to fit both straps' thickness, pull the straps over to close.