If you're using the egg white (or aquafaba), put that in the shaker first and give it a really strong "dry" shake by itself for 15-20 seconds.
Then add the bourbon, lemon juice, and simple syrup to the egg white in the shaker, and shake for another 15 seconds.
Last, add ice to the shaker and give the mixture another shake for 10-15 seconds (to cool it down, mostly, plus a little more emulsifying and getting a really good foam).
Strain into a rocks glass with fresh ice (you may add some of the ice from the shaker too if you want). You should have a good foam on the top.
Lastly, pour the red wine gently into the glass over the back of a spoon (this helps create the layer so it floats, vs. just pouring in directly).
If you're feeling fancy, you can garnish with a lemon slice and a maraschino cherry threaded on a cocktail stick.