Without getting into a detailed circuit design, there are a couple things to think about when using an AC source. Diodes will conduct only when forward biased, so with AC driving them, they’ll be dark half the time. That isn’t generally a desirable situation, so most people prefer to rectify the AC. A full-wave bridge rectifier is an inexpensive way to effectively double the brightness. Make sure your rectifier’s peak inverse voltage is larger than the supply peak voltage. The rectifier will cause about a Volt and a half reduction in your supply, so consider that.
The other thing to consider is that AC voltages are usually expressed in Volts RMS (root-mean-square). The concise explanation is that this allows power calculations to give the same results as for DC voltage. But the peak voltage will be higher (1.4 times higher) than the RMS voltage, so when you do rectify and convert to DC, you have to be sure to use the peak numbers.