Just went through this so I can provide the specific code as of bootstrap-vue v.2.5.0. This is from the docs, but as mentioned, it will take a little digging to uncover where all the paths are so I've included them all here.
create a _custom.scss file (I put mine in src/assets/):
// required:
@import "./node_modules/bootstrap/scss/functions";
@import "./node_modules/bootstrap/scss/variables";
@import "./node_modules/bootstrap/scss/mixins";
// optional
@import "./node_modules/bootstrap/scss/root";
@import "./node_modules/bootstrap/scss/reboot";
// @import "./node_modules/bootstrap/scss/type";
@import "./node_modules/bootstrap/scss/images";
// @import "./node_modules/bootstrap/scss/code";
@import "./node_modules/bootstrap/scss/grid";
// @import "./node_modules/bootstrap/scss/tables";
@import "./node_modules/bootstrap/scss/forms";
@import "./node_modules/bootstrap/scss/buttons";
@import "./node_modules/bootstrap/scss/transitions";
@import "./node_modules/bootstrap/scss/dropdown";
@import "./node_modules/bootstrap/scss/button-group";
@import "./node_modules/bootstrap/scss/input-group";
// @import "./node_modules/bootstrap/scss/custom-forms";
@import "./node_modules/bootstrap/scss/nav";
@import "./node_modules/bootstrap/scss/navbar";
@import "./node_modules/bootstrap/scss/card";
// @import "./node_modules/bootstrap/scss/breadcrumb";
// @import "./node_modules/bootstrap/scss/pagination";
// @import "./node_modules/bootstrap/scss/badge";
// @import "./node_modules/bootstrap/scss/jumbotron";
@import "./node_modules/bootstrap/scss/alert";
// @import "./node_modules/bootstrap/scss/progress";
// @import "./node_modules/bootstrap/scss/media";
@import "./node_modules/bootstrap/scss/list-group";
// @import "./node_modules/bootstrap/scss/close";
// @import "./node_modules/bootstrap/scss/toasts";
// @import "./node_modules/bootstrap/scss/modal";
// @import "./node_modules/bootstrap/scss/tooltip";
// @import "./node_modules/bootstrap/scss/popover";
// @import "./node_modules/bootstrap/scss/carousel";
// @import "./node_modules/bootstrap/scss/spinners";
@import "./node_modules/bootstrap/scss/utilities";
// @import "./node_modules/bootstrap/scss/print";
@import './node_modules/bootstrap-vue/src/variables';
@import './node_modules/bootstrap-vue/src/utilities';
@import "./node_modules/bootstrap-vue/src/components/card/index";
@import "./node_modules/bootstrap-vue/src/components/dropdown/index";
// @import "./node_modules/bootstrap-vue/src/components/form-checkbox/index";
// @import "./node_modules/bootstrap-vue/src/components/form-file/index";
@import "./node_modules/bootstrap-vue/src/components/form-input/index";
// @import "./node_modules/bootstrap-vue/src/components/form-radio/index";
// @import "./node_modules/bootstrap-vue/src/components/form-tags/index";
@import "./node_modules/bootstrap-vue/src/components/input-group/index";
// @import "./node_modules/bootstrap-vue/src/components/modal/index";
@import "./node_modules/bootstrap-vue/src/components/nav/index";
@import "./node_modules/bootstrap-vue/src/components/navbar/index";
// @import "./node_modules/bootstrap-vue/src/components/pagination/index";
// @import "./node_modules/bootstrap-vue/src/components/pagination-nav/index";
// @import "./node_modules/bootstrap-vue/src/components/popover/index";
// @import "./node_modules/bootstrap-vue/src/components/table/index";
// @import "./node_modules/bootstrap-vue/src/components/toast/index";
// @import "./node_modules/bootstrap-vue/src/components/tooltip/index";
As you can see, I commented out what I wasn't using. Then simply:
// in main.js:
import "./assets/_custom.scss";
Do not forget to include node-sass and sass-loader to use scss in Vue:
npm install --save-dev node-sass sass-loader
Note: You may need to adjust the SCSS import paths based on your build environment.