Welcome to BLF and welcome to "The Quest" ...for the best bike light.
I've been on this quest for newly 5 years and have found some very nice budget solutions.
Today, you have more choices than you probably want but there is hope.
1st of all, reconsider your choice of batteries. Although I respect your request, runtime and energy density go hand in hand when it comes to flashlights. Although it is easy to buy 3x AAA/18650 combinations, the 18650 will double your runtime. Since the option exists, I would have to say this is a good place to start.
You have 3 choices, basically... Cree Q5 (XR-E), R5 (XP-G), or T6 (XM-L). Each have their own plus's but if AAA is your battery choice, it pretty much limits you to the 1st one, XR-E commonly refered to as a Q5.
Just for reference:
1. XR-E are the default workhorse of bright LED flashlights. They can put out almost 300 lumens, 200 is more reasonable. Budget versions are very sensitive to battery sag as they will dim as battery life diminishes. These emitters are known to put out a very bright spot but little spill (which is useful for bikes).
2. XP-G wil another 50% brighter and very usable spill. They normally come in 18650 or 2x 16340 formats and they are considered quite bright. Budget XP-G lights still exhibit sag in the middle of the battry life.
3. XM-L are -bright- when driven hard. These are rarely AA/AAA driven. They are great emitters for almost any power level. They have great spill and even at 1 amp, they put out a lot of light, more than the rest. These are designed for 10 watts of power which is way more than most cyclists need. The nice thing about budget XM-L is that at lower power, they remain steady until nearly the end of the battery life.
Flashlights are typically designed to put out a very bright beam that will throw as far as possible. This is commonly done with reflectors. However, being seen on a bike means you would do better with a wide cone of light rather than a deep peering beam simply because the drivers wold have to aligned with you to see it. Unless you go with the power sucking XM-L at 800 lumens, the second best option would be a zoom style lens. Even the Q5 with little spill becomes and very wide bright beam. These lights are cheap and typically draw 1 amp or less. These are also the lights that have 3x AAA/18650 options. They are all over ebay.
So I will leave you with 2 ideas... one, a very nice bright bike light kit for a great deal:
XM-L bike light http://www.dealextreme.com/p/t6-assault-crown-waterproof-xml-t6-3-mode-1200-lumen-white-led-bike-light-with-battery-pack-set-82508
AAA/18650 zoomable light http://www.ebay.com/itm/Latest-CREE-Q5-LED-Zoomable-Flashlight-Torch-300-Lumens-/120672105065?pt=US_Flashlights&hash=item1c189e3269
Make on offer on the second one and you can probably get it for $10. I've bought from this seller multiple times.
Also don't miss out on the "18650" thread. Great offer for 18650 batteries in case you decide you want 4-6 hour runtimes on the zoomies. $17.50 +shipping for 10 quality cells.
Hope this helps and feel free to ask questions.