让你html里绑定一个动态的文字就好了：

<p class='container' id="app">
    <p class="dropdown">
        <input type="hidden"  name="amount" v-model="chosenAmount" value="">
        <button class="btn btn-secondary dropdown-toggle" type="button" id="dropdownMenu1" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false" >
            {{ chosenAmount }}
        </button>
        <p class="dropdown-menu" aria-labelledby="dropdownMenu1">
            <a class="dropdown-item" v-for="item in items" v-on:click="fillIn(item)" data-salary="{{item.message}}">{{ item.message }}个</a>
        </p>
    </p>
</p>

var amount = new Vue({
    el: '#app',
    data:{
          chosenAmount: '',
          items: [
              {message: '1'},
              {message: '2'},
              {message: '3'}
          ]
    },
    ready: function(){
        //这个初始化不能放在data里仅仅是因为bootstrap.js也会对data-toggle="dropdown"进行一些transform，那会覆盖掉初始化在data中的值。于是我们选择了生命周期的ready里，即在bootstrap处理之后再绑定初始文字
        this.chosenAmount = '请选择数量';
    },
    methods: {
        fillIn: function (item) {
            this.chosenAmount = item.message;
        }
    }
});

https://jsfiddle.net/hsfzxjy/esw77kjt/3/