Interesting you should cite Bill Bryson. We've been talking about his books on several boards here.
I avoid splitting infinitives, but it's not a sacred thing to me. If splitting an infinitive is less clumsy ("to boldly go..." in lieu of "boldly to go..."), I'll happily split away. I have a feeling this rule stems from Victorian grammarians who tried to impose Latin grammar on English. Latin infinitives (and those of most of its descendants) are, by nature of their being single words, unsplittable.