AP style says "spell out whole numbers below 10, and use figures for 10 and above".
Chicago Manual style says spells out numbers below 100, or as an alternative rule to use AP style instead.
Nielsen Norman Group says, basically, to heck with the old rules; everybody just skims online anyway so use figures for all specific numbers, because people notice those more. (hat tip to @Wanda for this one, which I had not seen before)
There's a reason these are called "style guides" and not "rulebooks". Be consistent, and you'll be fine.
(Personally I'd use numeric figures throughout for this case, because it's more easily distinguishable from the names in the list, and would make internationalization somewhat easier... but if pressed to change my mind on that I'd fold pretty easily.)
But this may not matter for your question, because:
If there's enough room to write either of "and 1 other" or "and one other", then (except for very long names) there's enough room to just include that other name itself...
✗ Bob, Ted, Alice, and 1 other
✓ Bob, Ted, Alice, and Linda
...so most of the time you won't need to start hiding values until there are at least two too many to show.
✓ Bob, Ted, Alice, and 2 others