The question title is misleading. You want to recharge your phone from the bicycle dynamo, and the AAA batteries are just a waystation for the energy to smooth out delivery to the phone. So you have multiple requirements for a circuit:
1) Accept input from the dynamo. Its output may be 6.0V while the bike is moving, but how does that voltage vary as the bike speed changes, or if its voltage output is regulated, how does the current output capability change with bike speed. What happens to your circuit when the bike is slow or stopped.
2) Charge a battery of some kind, which means the circuit must understand how to stop charging when the battery is full and stop discharging when it's empty (or the battery will be ruined).
3) Regulate the battery voltage to provide the proper output to the phone, which for iPhone means 5.0V at 500mA capability, along with some pullup/pulldown resistors on the data lines.
It's not clear how understanding all that, let alone designing, building, and testing it, is going to "save time" compared to buying something ready-made. Nonetheless let's take a look at what a circuit might look like.
The Minty Boost design mentioned above only does requirement 3). It's designed to take 2 x AA batteries and regulate their output to 5.0V for USB power. However it does not appear to turn itself off when the battery voltage gets below the "dead" threshold, so it's really only suitable to use with disposable batteries, as NiMH AA could be ruined if discharged below 1.0V per cell. For the same reason it wouldn't be suitable to use with Li-ion even if the 5.0V regulator still worked. The circuit does not accept power input from elsewhere nor charge batteries, so requirements 1) & 2) are unaddressed by Minty Boost.
To add battery charging, you'd need an additional regulator between the dynamo and the battery which limits voltage and current, and possibly controls charge termination depending on battery chemistry. For Li-ion you may use constant-current to constant-voltage charging which does not necessarily need a timeout, and also solves the problem that current into the battery may vary widely with bike speed. NiMH is harder to manage charging, and how to deal with fluctuating input to the charger may be difficult without making tradeoffs that dramatically shorten the cycle life.
With Li-ion you can pass the battery voltage through to the 5V regulator even while the battery is being charged, as fluctuating pass-through current only subtracts from input to the battery, which already fluctuates due to coming from a dynamo. For NiMH we already don't like fluctuating charge current so this issue only makes it worse.
You need a battery monitor circuit that at the least can turn off output from the battery to the phone when its voltage is too low. This is to say nothing of other safety features such as over/under-temperature, timeout, over-current protection with fuse or polyswitch, cell balancing if using more than one cell, and so on.
Overall you're looking at a decent sized project here, possibly months of work for a less-experienced engineer. Your question does not suggest a lot of experience and you may save a lot of time, money, and possibly be safer, buying something off the shelf.