First: Test Your Site
Use Google's own Mobile-Friendly Test page to see how user friendly your website is.
This will give you an indication of whether your site's mobile friendly or not, if it needs changing what to change and will also help you understand why your bounce rate is high (if that's a concern of course).
Second: Do You Need To Redesign
Once you have performed the above test you'll have an idea of whether a redesign of your website is necessary. You may well be mobile friendly but still opt to redesign for aesthetic or user journey or user experience issues.
Take a moment to review Google's own Mobile-Friendly guide page to see what's required and make an informed decision from there.
Still stuck or need guidance...?
Why not get in touch through Google+, mail or even phone and discuss your concerns.