React counter not incrementing, but adding 1 instead

I'm stumped, my react app isn't incrementing a counter as intended, instead of going 1,2,3,4,5, its going 1,11,111,1111,11111 ... My understanding is that you cant do this.state.count++ as that mutates the state which facebook says not to do, and they say to do this.state.count + 1. I'm fairly new to React and appreciate any help you can offer! Thanks!

import React, { Component } from 'react';
import './App.css';

class App extends Component {
  constructor(){
    super();
    this.state = {
      count: '0',
    }
    this.incrementCount = this.incrementCount.bind(this);
  }
  incrementCount() {
    this.setState({
      count: this.state.count + 1
    });
  }

  render() {
    return (
      <div className='app'>
        <div className='container'>
        <button onClick={this.incrementCount}>Click to increase bid: 
          {this.state.count}</button>
        </div>
     </div>
    );
  }
}
export default App;