@lightclock I'm really sorry for laughing out loud at the first "burn the house down" comment. It was pretty funny, but some of us on this thread have been insensitive about your genuine fear. Apologies x
British house spiders, I just let them go on their way, even if I spot a hefty one warily tippy-toeing across the carpet near me when I'm reading in bed. I don't think they mean us any harm, and there's no way on earth we're all chowing down on spiders while we sleep as scaremongers say.
Wasps and bees, on the other hand, turn me into a wafting, flailing, spectacle (mocked by friends) because I have a mild-ish but still unpleasant allergic reaction to bee stings. Slugs: harmless to me, but I'm gagging and retching at the sight of them, even thinking about them.
Cats are fantastic spider-hunters and spider-eaters, but of course that's a big commitment.
I'd go with a big, large diameter glass (not an opaque mug) and a large, stiff postcard plenty bigger than the glass. Hold the card tight under the glass, transport the spider into the garden. If it's nighttime and you have a good large glass, leave the spider under it until it's daylight, so it's less scary for you.