Thanks Alaska Mike!
I'm self-taught, by listening to Bill Staines, Roy Rogers (boy, could HE yodel!), Elton Britt, Frank Ifield (my first yodeling influence), the Sons of the Pioneers, Ranger Doug of Riders in the Sky, Rex Allen, Rosalie Allen, Patsy Montana, Kenny Roberts and many others.
The first thing is to overcome any embarassment you may feel at trying to yodel.
Seriously!
Then pick a song that you'd like to do. Something short and simple, not complicated, like Hank Williams' Lovesick Blues.
Sing along with the recording as closely as you can, until you can do it on your own.
If you can scream, you can yodel. Practise a Tarzan yell to find out if you can scream or not.
I mix up my "words" - syllables, if you will, when I yodel.
Sometimes it's the "Yodel-ay -ee - dee," sometimes I don't pronounce the "d" in "yodel."
So it's more like "Yolla - lay -ee - ee."
"Yolla - lay -ee olla -lolla - lay - ee; Ay -ee - olla lay - ee - oo."
And for variety, I'll occasionally throw in simple glottal stops with no consonants in the falsetto, corresponding to the syllables. This style is more prevalent in Alpine yodeling, and it's damn hard to write.
I practise my yodeling a lot in the car, on the way to or from gigs. Unless I have company of course!
Give it a go, and don't worry about the begrudgers.
By the way Alaska Mike, Rex Allen was a sorta bass-baritone kinda singer, like yourself, and he was a brilliant yodeler.

Seamus