I would cut a stem and remove the bottom leaves and blooms, treat with a rooting hormone and let the cut callous for a day. Keep the top part in a baggie so it won't dry out. Pot up in Perlite and keep a plastic tent over it. You could try water rooting a stem as well.

I have rooted tuberous in the past this way but there are probably much better ways. I have gotten out of growing Reiger and tuberous because they are difficult for me to keep. Most people treat Reiger begonias as annuals for this reason.

I know this is old now, but in case anyone finds it helpful...

I treat cuttings the same way as all other begonia stem cuttings; just as hcmcdole says above, except that I put the cutting into light potting mix immediately, and keep it under plastic in bright light until it starts growing. My "light" mix is equal parts perlite, peat moss, and vermiculite, or lately just half to 1/3 CocoBlend potting mix, and half to 2/3 perlite. Often as not the first growth you notice will be flower buds.

I remove flower buds for a few weeks while the plant establishes, taking the cover off partly, then a little more, over a week or two to harden it off.

Starting begonias of all kinds became easier and more reliable for me when I began starting them close under fluorescent lights. Despite what I've read, Reigers don't seem any more difficult to root than the average Begonia.

Starting Reiger cuttings in Fall and keeping them as small houseplants overwinter is the easiest way for me to keep them going.

Vincent