Halachipedia citing O.C. 317:5, and other sources, says:
- A bow-knot, slipknot, or a single-knot isn’t a true Kesher-bind and is permissible even if it does remain in place for a while. [21]
For example: a ribbon on a gift, a single bind on a shopping bag or
garbage liner.
- It is permitted to tie a slip knot or bow without a underlying knot even if it is tight and meant never to be undone. [22]
- After tying a bow knot (a bow on top of a single knot), as is common when tying one's shoes, one may not tie a second bow on top of
the bow knot. [23] Others permit tying this knot since it can still be
untied with a single hand by pulling on the end of the string. [24]
Further:
Many authorities hold that it is permissible to tie a necktie on
Shabbat if one usually unties it within 24 hours. However, if one
doesn't usually untie it within 24 hours, some say that if one intends
to untie it within 24 hours it is permitted, while others write that
one should tie it from before Shabbat and put it on and take it off by
just tightening and loosening the side which goes around the neck,
however, one shouldn't untie it on Shabbat
Having stated this, I am aware that there are a few ways to tie a bow tie as well as a regular tie. Looking at the diagram on this page, as well as watching how my shul's chazzan makes his bow tie, which pretty much follows the diagram, this looks like a slip-knot or bow which unravels quite easily with a simple tug. Based on that style of bow, it seems to match up with what Halchipedia says is permitted on Shabbat.