AFAIK all trekking bars are wider than you specify. Even Modolo Dumbo with adjustable width narrows down to minimum 54cm c-t-c (unless you hack it).

Here's an alternative to a bullhorn. Take an inexpensive 3-5 degree bend MTB flat bar, cut ends off (with hack saw or tubing cutter) to desired width, and add ~12cm long bar-ends. This will approximate the geometry of a bullhorn bar while enabling use of existing controls, at relatively low cost. Note the size bar needed for compatibility with your stem (25.4 or 31.8mm). A bar which tapers to the diameter required for MTB lever/shifter mounting (22.2mm diameter) in the shortest distance is preferable as it permits narrower control location, narrower overall bar width, and may leave room for accessory mounting. 25.4mm bars are usually better in this regard, as 31.8 bars have a larger center bulge which takes 9-15cm to reduce diameter.

Google "flat bar with bar ends", then click images tab, and you'll see dozens of examples.