How can I pre-wash/dry bolts of fabric in a way that will prevent the cut ends from unraveling?
To prevent fraying, use a z-stitch (zig-zag stitch) with a standard sewing machine or serge the ends of the fabric before you wash it.
I've recently read a lot of guides about washing fabric before sewing and, while they often disagree about whether washing is necessary or not - generally depending on the type of fabric and the end use, the one thing they pretty much universally agree on if you are washing fabric, is that if you want to prevent fraying, stitch the cut ends. Some sites don't seem to be bothered by fraying and recommend simply cutting the strings off afterwards but this seems like a great way to get your fabric tied up in knots.
One guide notes to consider the weave tightness:

First, remember that fabrics will fray depending on how tightly they are woven.  Loosely woven fabrics like Linen and some cottons can fray a 1/2 inch or so.  But some cottons and polyesters with a tighter weave might only frizz out on the ends.  And knit fabrics won’t fray at all.

Other common notes are:

wash the fabric in large pieces rather than small ones as the small pieces can be sucked into the machine's agitator
wash the fabric in the same method you plan to wash the garment - so (as an example) if you're planning to dry clean your wool, dry clean the fabric rather than machine washing it.


As a note, with all methods, your results may vary. This quilting site has a forum with a topic where many quilters are discussing preventing fraying and the results are mixed.
Different methods mentioned include clipping the corners, using pinking shears, sewing/serging, and simply not doing anything at all because fraying is inevitable... so the top suggestion is to always make sure you have extra fabric to allow for losing an inch or two to fraying.
Here are a few of the comments I thought seemed helpful:

auntpiggylpn: I also tried the &quot;Clip the Corners&quot; method and my fabrics still frayed, didn't seem to be any less or more than if I did nothing to the edges. This was also LQS type fabric. I tried the pinking shears trick and it didn't stop the fraying. I've also sewed along the edges prior to washing but it still frayed. Some fabrics don't fray at all and then some others I will loose at least an inch off the total cut. I ALWAYS was in cold on a delicate cycle and only put in the dryer until damp them iron. sorry, I don't have any positive answers for you!!
MaryAnnMc: I agree, everything I've tried still frays. But I've decided to stick with pinking: it does cut down on the fraying considerably, and I can always tell which fabrics in my stash have been washed. that alone is a good reason.
M.I.Late:I also just let it fray and just rip off the threads. When I wash fabric, I open it all the way up. I find that some manufacturers don't get it rolled on the bolt completely straight. So, I open it up completely, wash and dry it, refold it so there are no diagonal waves when held selvage to selvage, (I usually lose 1-2 inches here - but it has been as much as 3.) Then I trim it with the rotary cutter and iron it and it gets either used then or stashed for future use.
bearisgray: I finally learned to either serge the raw edge or overcast the raw edge with a long, narrow zigzag stitch before washing. I lose - at the most - about 1/8 inch of fabric when I zigzag the edges - none when I overcast if I remove the stitching.