Media queries combined with the viewport meta-tag solves your problem.
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
Using that meta-tag, phones will respond to media queries around 240-360 pixels, depending on their screen size.
I like to use bootstrap to not be bothered with media queries myself. But I only use small parts from bootstrap, and I opt-in/opt-out from specific parts by removing/adding includes to specific modules from bootstrap. (you can do that with the LESS or SASS version of the package, copy the generic "imports" file, and comment-out everything you don't want/need)
Bootstrap includes many sane defaults and some fixes for weird browsers. By choosing what to include and what not to include, I can choose whether I want bootstrap's opinionated styles or my own, and I can switch later (start out with bootstrap forms, customise them later & finally remove bootstrap form styles)