The current release of bootstrap-vue (v2.21.2) only supports Vue 2, but there's a GitHub issue tracking Vue 3 support (bootstrap-vue Issue #5196).

In the meantime, there is a third-party version that supports Vue 3:

1. Install bootstrap and bootstrap-vue-3:

npm i -S bootstrap bootstrap-vue-3

1. Initialize bootstrap-vue-3 in main.ts:

import { createApp } from 'vue'
import BootstrapVue3 from 'bootstrap-vue-3'

// Since every component imports their Bootstrap functionality,
// the following line is not necessary:
// import 'bootstrap'

import 'bootstrap/dist/css/bootstrap.css'
import 'bootstrap-vue-3/dist/bootstrap-vue-3.css'

const app = createApp(App)
app.use(BootstrapVue3)
app.mount('#app')

This package is deprecated and the repo was moved to bootstrap-vue organization. https://www.npmjs.com/package/bootstrap-vue-3

Here is the installation process of bootstrap-vue

# with npm
npm install vue bootstrap bootstrap-vue
# with yarn
npm install vue bootstrap bootstrap-vue

Then, register BootstrapVue in your app entry point (typically app.js or main.js)

import Vue from 'vue'
import { BootstrapVue, IconsPlugin } from 'bootstrap-vue'

// Import Bootstrap and BootstrapVue CSS files (order is important)
import 'bootstrap/dist/css/bootstrap.css'
import 'bootstrap-vue/dist/bootstrap-vue.css'

// Make BootstrapVue available throughout your project
Vue.use(BootstrapVue)
// Optionally install the BootstrapVue icon components plugin
Vue.use(IconsPlugin)

You can also follow the bellow link. https://bootstrap-vue.org/docs#using-module-bundlers