The closest thing I've found to vegan 'milk' chocolate is the 'boom choco boom' ricemilk chocolate bar. I get them at Wegmans. The ricemilk chocolate bar (purple wrapper) is certified vegan, but the crunch bar is not - just so you are aware. I am not sure why, it still says it is dairy free, but it just isn't certified vegan. They have a website too, all the ingredients are listed if you want to check it out, just google 'boom choco boom' and it should come up.
You could also make your own chocolate 'milk' - using cocoa powder and adding as much of your favorite milk alternative and sweetner to your own tastes.
Also if you do have access to Wegmans - their semi-sweet chocolate chips are vegan, I like to keep a stash of those around for a quick, cheap chocolate fix - but they are closer to dark chocolate, so I'm not sure if you would like them as much. They are definitely not bitter, but not quite 'milk' chocolate. They have an organic version which is also vegan, but I think the non-organic actually tastes better.
Ben & Jerry's has a line of non-dairy certified vegan ice cream, one of which is a chocolate fudge flavor.
Those are my go-to's for chocolate cravings, hopefully it is helpful for you!