Firstly, I am an oil and gas analyst by trade. I do macro work for the price of oil globally. Essentially, I actually writes articles on this subject.
This will do absolutely nothing to affect oil prices. Nothing what so ever. Zip. Zilch. Ha. Ha. Ha. Ha. If you want to help drop oil prices, buy a bike, power your house via solar, avoid big box and franchise stores. This plan has so many flaws that I find it hilarious.
Right off the bat, transportation only accounts for 28% of energy use in the USA. Essentially, whatever effect you think you had on the effect of oil prices, you can more or less immediately cut that to a quarter. This is only if you don't use the actual gas on that day. Buying the petroleum on the day does nothing. You would actually have to cut your consumption of petroleum on a day. If you manage to use a 1/4 of your normal gasoline used for travel by taking public transportation, congratulations, you've cut your total petroleum use by 21%. Wait though, you know all that food that is in your fridge? It was shipped in a truck to the store where you bought it, probably from 1,000's of miles away. Everything you purchase was shipped in trucks. The mail you receive was shipped in trucks. This is where a huge bulk of "transportation" use comes from. If you cut the amount of gasoline you use to 25% by using more public transportation, bicycles and carpooling, its doubtful you're cutting your energy use by even 15%, for a single day.
Lets do a little math here. The United States uses ~21,500,000 barrels of oil per day (boepd). The world uses ~85,000,000 boepd. Suppose you were able to cut your energy use by 15% for a single day. Lets suppose EVERY American consumer participated in this activity. The United States has used 18,275,000 boepd on this particular day (21.5MM boepd *.15). This gives a surplus of 3,225,000 boe. The world goes through this much oil in less than 55 minutes. The surplus oil would be injected directly into the inventories of the United States and giving a HUGE boost of less than 1% of total American oil inventories. This would probably not affect oil prices by a goddamn penny. Not a single cent.
However, a 15% cut in energy use is actually quite commendable over the long term. This would affect the price of oil if enough people were to cut their usage. Most developing nations do not give a fuck about gas prices or emissions. India and China will continue to have a great affect on oil prices year after year. Buy a bike, buy a hybrid, shop locally if you want to have an affect.