Show/Hide ReactJS components without losing their internal state?

One option would be to move the conditional inside the component itself:

Bio = React.createClass({
    render: function() {
        if(this.props.show) {
            return <p>bio comp</p>
        } else {
            return null;
        }
    }
});

<Bio show={isBioPage} />

Whether this is “best practise” or not probably depends on the exact situation.