When the mind is free of worries, the legs can do their best work.
One of the best strategies for removing worry from my rides is preparation. Over the years, going for ride after ride, one develops a rhythm and cadence not only while on the bike, but to the other activities that support riding frequently. The Brita filter is refilled every couple days; laundry is washed on days bounded by a ratio between the number of bibs owned and the frequency of rides; the steed is cleaned and lubed.
In the words of legendary basketball coach, John Wooden, "Failing to prepare is preparing to fail."
Prior to each ride, the bike is gone over, ensuring tyres are at the desired pressure, brakes are operational and don't rub, and bidons are filled. If I'm going on a longer ride, one bidon will often be supplemented with a protein/carb mix, and this will always be placed in the seat tube cage. I won't have to concern myself during the ride with where my calories are - when I reach for them, they will be there.
Occasionally, despite the best preparations, a flat or other mechanical will be suffered, but if one brings the right stuff, one needn't worry about anything other than having to change a tyre for 5 minutes. I've distilled what I carry down to: a pair of tyre levers, spare tube, patch kit, pump, multitool, and a ziplock bag into which I put my cell phone, a spare, expired ID (that still shows who I am and the correct address to bring my lifeless body home to, should it come to that), and one single key to get me back into my garage. I used to add my wallet and full set of keys, but that extra weight just slows me down.
Similarly, when weather conditions may be inclement, it's good to pack arm and leg warmers and a rain shell into the jersey pockets. These are always to be rolled up starting at the bottom, so when I grab them out of a back pocket during a ride, I can hold onto the end, unroll them, and know that the part I'm grabbing is the top of the arm warmer or the collar of the jacket. I don't have to worry about sorting out how to put it on mid ride.
Together, these details evolve into a ritual series of preparation that function to remove doubt and worry from the ride. They are, over the years, distilled down to cover only what is needed, leaving everything superfluous behind.