First, a safety warning
25 IR LEDs at 100 mA each will be a LOT of IR radiation. If they're close together, your pupils are dilated (indoors, this is often true), and/or you're close to the matrix, you could really hurt your eyes.
The image of the matrix will be focused to a tiny area on your retina, and you'll hear/feel a little pop as the blood and fluid there boils. You'll have a permanent blind spot. Not fun. BTW, it's your job to make sure that you understand what you're doing and don't hurt yourself, not mine. I'll help you begin understanding, but I won't be held responsible.
My advice: For development (and production if possible), put bright green LEDs in series and physically close to the IR LEDs so that your blink reflex is activated at a bare minimum. Use hardware (in addition to software) techniques to limit the number of LEDs lit and/or the power delivered to the matrix to help ensure that only one LED is on at a time.
Techniques
There are many LED driving techniques. None of them hinge on delivering 1.35V; that will change between LED batches, over time, and with temperature.
If you're just interested in current limiting, a few transistors will be sufficient. The total transistor count will depend on your choice of a current limiting circuit topology, which is dependent on your heat sinking capabilities, routing area, and other contstraints. There are also voltage/current regulation ICs and linear LED drivers which would simplify your job. If you're interested in power conservation, many buck converters can be configured for current limiting, which would maximize your battery life.
You may want to have unlimited sink and limited source (or vice versa). Alternatively, you might have just one current source, and mux it between the various LEDs. Because of the safety issues inherent in this project, I'd recommend the latter option.
Power seems to be an important aspect in your design, so you might consider using different LEDs. Low-current LEDs for instance take 2mA instead of 20mA.
Or maybe 5mA through your existing LEDs will produce enough light for your taste.
Another angle would be to design your LED drive circuit for as low a voltage as you can. If you can design it for 3V and you use a switched power supply to create this 3V from 5V (or maybe 12V), you have saved 40% energy. This is especially effective when you use a battry, which produces a lower voltage over time.
I guess that when you want to iluminate (nearly) all LEDs you can get by with illuminating them each a bit less. This logic could be incorporated in your software, so the worst case current would be reduced.
You must design your circuitry for the worst case, but for battery life it might be more realistic to calculate with averaged cases. So get some more info on what you want to show when you need to know how a given battery will last.
As often, your one good question results in an avelange of questions, and some questioning of your basic assumptions. That's system design :)
Best Answer
It looks like you are reviving an old 50cc, trying to work around the front light and flashing relay that end up failing forever... Yes, a bridge 10-30A rectifier, and a overhauled boost converter is the clean solution, but consider input voltages beyond 60V (90V is not rare).Even so, in idle the rotor rpm is low, may float the lights, even leds, even arduino... The dirty solution is to add a Little (1Ah) 6 or 12V Battery in the bike, charge it with one diode from one pole of alternator in series with a relay ( arduino will control the charge) beeing N.C. of relay connected directly to batery, and N.O. connected to battery via 1,8 Ohm wire resistor ( charging low in high rpm). Alternatively, charge directly via 10A triac, controlled by arduino, taking care on trigger angle, or you end up having to install a stronger battery. Shall you master your arduino, you can even control the second pole of alternator to drive the correct ~voltage to the 10W LED via another triac and series resistor (some 10 Ohm to not let the Led face to face with alternator\triac bursts).This frees you to control the four 3W Leds the normal way (common NPN transistors, open collector in series with each 3W Led, four arduino pins, one for each transistor base, via 2-10K resistors). Make this circuit breath, cause it's hot!!!