This is how I was told many years ago (by an old musician named "Sweet Louie") (and it worked, although it took me a number of tries to get it to do so) (A wine called Mateuse was "en vogue" among younger people back then, and I had all of my friends, who thought I was crazy, saving their empty Mateuse bottles for me!). Take an appropriate bottle, dip a thick piece of absorbant string (years ago almost all string was made of cotton which is pretty absorbant). Dip the string in lighter fluid and wrap it around the bottle-neck just slightly farther than where you want the break. Light the string, let it burn out then quickly dip the bottle in cold water. The neck will then come off (

) (sometimes a few taps are necessary). If you're lucky the break will be fairly clean. You can smooth out the broken edge (and this
is the best way) by rubbing it back and forth on a concrete side-walk, street-pavement or cinderblock. (Sandpaper, etc is much too fine and something like an electric-grinder will "spot-heat" the glass and chip it away as you try to grind it smooth, so rubbing it on concrete really is actually the best way.)
If you finally give up trying to get the semi-clean lit-string break (which I almost did give up, but luckily on what would have probably been my last try it worked!) you can also just start breaking the bottle away a little at a time with a small hammer until you get to the neck and then just keep on rubbing (and rubbing!) the broken-off neck on the concrete until you get it where you want it (which is how a lot of guys do it who have chosen to... "dabble in nostalgia"

).
In all honesty a good store-bought slide is just as good, if not better. Thirty-five or so years ago when I first got into acoustic blues slide you couldn't find slides in music stores (except for the very thin chrome-plated metal ones for electric-guitar you could occasionally find, which weren't very good for acoustic. In the words of Fred McDowell when I first showed him the slide I'd bought to learn with..."Hahaha! That'll never do!" and then he got an old un-plated steel deep-well socket out of the tool-box beneath his tractor-seat and gave it to me to use for a slide.) There was no choice back then but to make one from a bottle-neck or a piece of pipe or medicine or extract bottle (or a deep-well socket!). Nowadays as the country-blues and Delta-slide genres have gotten much more popular there's a pretty big selection of slides around to choose from, both good and bad. I have a couple of boxes of slides, many homemade and quite a few store-bought as well, made from all different kinds of materials and thicknesses and sizes, from glass to brass to solid gold. They all have their own feel and musical quality (a fairly short, medium thickness brass is usually my favorite). But I completely understand why you'd wanna try making your own. Good luck!