There is always discussion on here about washing VS not washing. I wash evey batik I bring into my house. I use hot water, detergent, and color catchers, and sometimes vinegar which is supposed to set your color. Generally I only wash once, however, on a couple of the in-expensive batiks, I have had to wash again.
I have a friend who thought she had washed a batik she used, (mottled purple/green/burgundy). When she washed the quilt, the burgundy ran into her white. She spent many hours working to "clean" her quilt. She was mostly successful in getting it out, but if you look hard you can still see where it ran.
I had a LQS employee tell me the manufacturers boil the batiks to get the wax resist out of them, which should make them not run color, but my experience has been different.
If I am washing a fat quarter, or smaller, I use my lingerie bag to help protect them on gentle cycle, hot water, etc. Also, I may start them out in the dryer to help them dry faster, but DO NOT run them the entire cycle. They fray terribly. With your 2.5 strips, I might just hang them and press.