One great thing about eating on a bike tour is that on most tours you never need to carry more than a days worth of food. So it doesn't weigh you down too much or need to keep very long.
The foods you mentioned are a good start. Regular bread will keep for a few days, tortillas will keep for a month, crackers with keep for decades. If you like milk, either to drink or on your cereal, Nido powdered whole milk is great, also there are ultralong shelf life cartons of milk. If you buy regular milk it will still be fine to drink a few hours later. Avocados, carrots, and other veggies keep for a while. Shredded cabbage keeps pretty long as a lettuce substitute in wraps. Freeze dried hummus is pretty good and you just add water. Hard cheeses look nasty if kept in the heat but remain edible.
Another option is to just pick up a subway sub or a sandwich from a grocery store, deli, or diner earlier in the day.