How do they print bolts of fabric?

They go through presses just like paper. The more colors, the more rollers that hold the patten with the color. Same thing as your local news paper does.

What is the term for this process, 'rotary press'?

Here's just one of the ways its done.

[media]http://www.youtube.com/watch?v=6iVicNDx-00&feature=related[/media]

It' like a rotory press. Same process. Paper is printed using large rolls of paper that go through the four color process and then cut and folded after printing. Fabric is printed in the same manor but left on the rolls. Then it goes to the garment mfgr. to be cut and made into garments.

found a good article on rotary presses, very good info
Get Production Rolling With Rotary Screen Printing | ScreenWeb | screenweb.com
this cleared up allot of misinformation for me.

Drum / rotary printing is used for large quantities (full bolts, factory quantities of production, etc.)

For medium quantities, it can be flat printed on fabric tables using automatic screenprinting equipment.

For small runs / boutique production, etc. it's usually done by hand-screenprinting it on fabric tables. This is a lot more practical than you would imagine.

These days, small quantities are also done using wide-format DTG printers.