You will just need 5.25 Liters (3 1.75L bottles) of Everclear. Ever clear is 151 proof. If you mix 5.25 L of Everclear and 14.75 L of water you will have 20 liters of 40 proof neutral spirits which in my opinion would be enough to season the barrel.
That would cost you about $100
Most bourbons are in the 80 proof and up range. To make 80 proof neutral spirits it would take 10.5 Liters of Everclear 151 in your 20L barrel.
I would say that you could possibly go as low as 30 proof (15%) and not worry about contamination of the barrel while you are seasoning the barrel.
My wife got me a 10L barrel for xmas last year. Like yours, it was a virgin medium char barrel. I created a blend of Everclear, Grey Goose Vodka, White Rye Whiskey, Ranger Creek White Whiskey and water to season my barrel. After 3 months, I pulled the whiskey and put a porter in the barrel. After 3 months, I pulled the porter and put a Quad in the barrel. After 3 months, I pulled the Quad and now have a Wee Heavy in the barrel. I brew a larger batch and use 500ml swing top bottles to hold uncarbonated beer to top off the barrel from evaporation. This also allows you to have a comparison of the oaked beer and unoaked beer. My porter was probably over oaked. My Quad is pretty tasty and at 1 month in the barrel my Wee Heavy has a very faint oak flavor so I'm thinking the barrel is done with providing flavor and is ready for some sours. I keep my barrel next to fireplace in our family room so it does experience temperature extremes. On average it would evaporate about 350ml over a month period.
My advice is to experiment and have fun. I never asked for advice here since everyone seems to think you can't do anything with a small barrel.
What I have learned.
Plan ahead where you plan to place your barrel if you can't lift it. I'm guessing it should not be too much work to carry a 20L barrel. I have no problems moving my 10L barrel to fill up or to move to the kitchen for bottling.
Brew 2 to 3 gallons more beer to bulk age unoaked. This can be used to blend if you over oak the beer.
Plan to make a mess on filling days, topping off and sampling. You will notice that I have a Vinny Nail that I use to get samples. Unfortunately, this is pretty messy.
If you bottle you will have to prime with more sugar since the beer gasses off CO2 pretty fast in the barrel. The Porter was in the barrel for 3 months. I primed it for 2.5 volumes based on calculators but it is more like 2 volumes. With the quad, I primed for 3.3 volumes knowing that it would actually be closer to 2.8 to 3.