Using a linear voltage regulator like an LM317T is a decent idea, but it means you're guaranteed to throw away 2 V, which is a little disappointing. You might instead try a low-dropout regulator like the LT3085-- with that, you'd only lose 0.275 V.
But in both cases, you'll be limited by the relatively low current limit of the regulator (1.5 A for the LM317T, only 500 mA for the LT3085). For a bike light, either would work fine, but I think you could build a more robust circuit without a regulator.
Here's what I'd suggest.
First, cap the voltage with a 13 V zener diode between power and ground. A zener diode is a diode that acts mostly like a normal diode-- a one-way valve. However, in the no-flow direction, it blocks current until you hit a certain threshold voltage. Once you hit that voltage, it opens up with very low resistance until you drop below the threshold again. It's great for capping voltage spikes. Be sure to get one that can handle the power you'll me pumping through it. Maybe start with a 5 W diode and then buy a fatter one if that burns?
Second, you need to limit the current through the LEDs. (If you did this part right, you might not even need the zener, but zeners are cheap.) LEDs burn out because they get too hot, and prolonged high current is what makes them hot. They can handle very high currents for short periods. Whatever LEDs you buy will have a current rating, like 20 mA at 4 V. There are no LEDs with voltages over roughly 5 V. The higher voltage LEDs you see advertised are either multiple LEDs in series or LEDs packaged with a current-limiting resistor. You can do better with discrete LEDs.
What you should do is put LEDs in series until you get close to your supply voltage-- maybe 3 of them, so you're trying to supply 3 * 4 V = 12 V, 20 mA. Then, take the remaining voltage between the cap (13 V) and the LED voltage (12 V) and pick a resistor that allows the right amount of current. In this case, 13 - 12 is 1 V, and you want 20 mA, so that's 1/0.020 = 50 ohms. I'd build one string like this and test it. Once that's working, build a few more. You can tweak the resistor value to make the LEDs a little brighter or dimmer (but don't burn them out).
Putting LEDs in parallel without giving each series string its own resistor is risky. LEDs are nonlinear elements-- raise the voltage a little near a certain threshold and the current changes dramatically. This means that they tend to not share current evenly. You might be able to pull it off if the LEDs are all from the same manufacturing run, but resistors are almost free; I wouldn't think it would be worth the savings.