"A Bushel and a Peck" is a song written by Frank Loesser for "Guys and Dolls".
A bushel is a unit of dry measure equal to 64 pints. A peck is also a unit of measure for dry material equal to 8 quarts. Both are also names for the containers that hold that unit of measure.
In the below lyrics there is the mention of a farm so perhaps the bushel and peck aspect have to do with farming and the containers for holding dry goods, i.e., corn, apples etc. In other words, the person in the song is expressing their love for the other person and the love is measured by the large capacity of the containers. But it's only a guess as the lyrics are a little goofy and silly. You would probably have to read something about the song writer and why he came up with the lyrics.
I think your father just mixed up the lyrics a little and added the word "gun" to the song he sang to you as a child, or you misheard what he was singing.
"I love you a bushel and peck
A bushel and peck and a hug around the neck
A hug around the neck and a barrel and a heap
A barrel and a heap and I'm talking in my sleep
About you, about you
Cause I love you a bushel and a peck
You bet your pretty neck, I do
Doodle, oodle, oodle, doodle, oodle, oodle, doodle, oodle, oodle oo
I love you a bushel and peck
A bushel and peck though you make my heart a wreck
Make my heart a wreck and you make my life a mess
Make my life a mess, yes
A mess of happiness
About you, about you
Cause I love you a bushel and a peck
You bet your pretty neck, I do
Doodle, oodle, oodle, doodle, oodle, oodle, doodle, oodle, oodle oo
I love you a bushel and peck
A bushel and peck and it beats me all to heck
Beats me all to heck and I'll never tend the farm
Never tend the farm when I wanna keep my arm
About you, about you
Cause I love you a bushel and a peck
You bet your pretty neck, I do
Doodle, oodle, oodle, doodle, oodle, oodle, doodle, oodle, oodle oo"