Avoid root veg, they're full of carbs, carrots to an extent, try leafy greens or above ground veg. Bread will cause you a spike there isn't a slow release etc, it will convert into sugar no matter the colour or grain. If you start now, within 24hours you will see the difference of a low carb diet. Yes the metformin may have you worried but if it helps you for now to get down within range, take it.
After a cycle ride one would expect the muscles to burn glucose so you can't rely on this alone. I'm normally 4-6 these days without needing to exercise, and when I do exercise i'm nearing hypo range.
Listen to the advice on here, Dieticians and Doctors alike haven't updated their advice and it's very misleading at the beginning of diagnosis.
Definitely try a low carb diet. No potatoes, rice, pasta, bread or anything made from flour, includes pizza, pita bread, tortillas etc. Look up low carb. How much you do depends on how quickly you want to get rid of your diabetes. Replace your carbs with healthy fats like cheese, avocados etc. I do less than 20g carbs a day.
Do listen to the advice on here, it will save you a lot of trouble and headache.