As with all engineering problems, it depends 
How much accuracy do you need? What load currents (beyond the Arduino) will you be pulling from the supply? etc. etc.
Maybe it's easiest to just try it. Look at the voltage waveform on the AC side (carefully...don't do it if you don't know what you're doing and what an 'earth-grounded oscilloscope' is, or maybe you have an isolated voltage probe), then look at it on the transformer side and see if the waveshape is preserved by your transformer. Then hook up your bridge rectifier and capacitor and a dummy load (100 ohm 2W power resistor might be a good load) and see how it changes. Too much? Then go to plan B.....
Of course, "looking" at waveforms is not a measure of quality (looking at total harmonic distortion on a spectral plot is better) but at least it's a start.
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The Arduino Drum Machine: MIDI development system with 14-track MIDI drum machine sequencer / groove-box software