Testing for AC ripple...

I know an oscilloscope is ideal but all I have is a good DMM.

I can test for AC voltage over a DC circuit with a DMM. Is that the same as testing AC ripple and is the data extrapolated from the DMM accurate enough to be useful?

Unfortunately the DMM won't be accurate enough or have a response time fast enough to show AC ripple at high frequencies. There's no substitute for a scope in this kind of thing I'm afraid.

At high frequencies, my DMM gives really strange readings that drift all over the place and have almost no relationship to the AC voltage.

You could make a thing to convert AC to DC, but I think that it would have to be powered because the ripple voltage is usually lower than the voltage drop across a diode. www.epanorama.net or www.national.com may have something under "precision rectifier".