To avoid yarn wastage due to the multiple colour changes keep ends short. I prefer to cut off the old colour and firmly tie on the new colour then continue knitting. This has the added benefit of far fewer tails to darn in.
Felting is incredibly forgiving and there is no need to worry about the stripes looking uneven.
Ladder stitch the seam, by picking up alternate threads on each side of the very edge of the knitting. This will void a bulky join and create a seamless hot water bottle cover.
3 needle cast off -Slip the first 19 sts onto a spare 8mm needle.
Put both needle points together so that the hot water bottle cover lays flat with the decreases creating the cover shaping at the sides.