E.B.
A sprig, for most culinary uses, is one single stem of an herb. For example, a sprig of thyme will have one main stem at the bottom, and several small branches that are attached. A stem with lots of little stems attached would be a large sprig, and a stem with just one or two smaller stems would be a small sprig.
For a bunch of thyme in a sauce, if your sauce will be at least a couple of quarts (as opposed to a very small serving for just one or two people), I'd use the standard American cigar as a reference (not those big old fat hand-rolled Cuban monster ones). You want enough sprigs to look like a cigar when tied loosely together.
Thyme is usually added early in the cooking process. It has a tough woody kind of stem, like rosemary or oregano. Herbs with woody stems generally can take longer cooking, as opposed to herbs with grass-like, delicate, bendable stems (basil, parsley, etc). Those kinds of herbs are usually added at the end of the cooking time, or just before serving.
It's generally preferred to tie a bunch of thyme (or other herbs that won't be consumed, but are intended to impart flavor) with kitchen twine or string so that you can remove the herb easily.
Hope that helps. I love bolognese. Are you putting chicken livers in it? Now I want bolognese!