Bottom Dollar (“Bet your bottom dollar”)

“Bottom dollar” means one’s very last dollar. To “bet your bottom dollar” means to bet even one’s last dollar, such as the bottom dollar in a stack of dollars at a gambling table.
 
“Bottom dollar” has been cited in print since at least 1855 and “bet your bottom dollar” since at least 1856. “Top dollar” (cited in print since at least 1921) means the most dollars, or the “top dollar” amount.
 
       
Free Merriam-Webster Dictionary
bottom dollar noun
Definition of BOTTOM DOLLAR
: last dollar “you can bet your bottom dollar”
 
The Free Dictionary
you (can) bet your bottom dollar
you can be very sure If there’s anything he can sue you for, you can bet your bottom dollar you’ll be in court.
Etymology: based on the literal meaning of bottom dollar (your last bit of money, which you would not risk losing)
 
(Oxford English Dictionary)
bottom dollar n. U.S. (one’s) last dollar, usu. in collocations with bet.
1857 San Francisco Call 24 Jan. 4/1   Sometimes, however, luck will run against him, and‥he ‘slips up for his bottom dollar’.
1866 Congress. Globe Mar. 1474/1   His opinion is that a State can go out of the Union and he is willing to bet his bottom dollar on his judgment.
1904 W. N. Harben Georgians v. 43   You bet yore bottom dollar I’m open to criticism myself.

7 February 1855, New Orleans (LA) Daily Picayune, “From Mississippi,” pg. 1, col. 3:
There is not a man among their friends who would not go his “bottom dollar” on them, as will be seen by their sticking to them if they resume, which it is presumed they will.
 
Google Books
The Creole Orphans or Lights and Shadows of Southern Life
A tale of Louisiana
By James S. Peacocke
New York, NY: Derby & Jackson; Cincinnati, H.W. Derby
1856
Pg. 197:
There are many other parties we might point out: the fast cotton planter, who having just got through the bottom dollar of his crop, and the last one his merchant would bleed, is now about to leave on the Sunday packet for the coast and the little towns above;...
 
16 September 1856, Galveston (TX) News, “One of the Polk Men,” pg. 1, col. 7:
“I’m going to vote for you (James Polk—ed.)—you can bet your bottom dollar on that!”
(...)
—St. Louis Herald.
   
20 August 1859, Freedom’s Champion (Atchison City, KS), pg. 1, col. 3:
And whenever you come across anything that the opposition have done that looks more black-hearted and tyrannical than anything you have ever heard of, just bet your bottom dollar that by looking up the record you can find deed just as bad, and “ten times worse,” that must forever lie at the door of Democracy.
 
22 September 1859, New-York (NY) Commercial Advertiser, pg. 1, col. 9:
From the New Orleans Christian Advocate.
(...)
The young one replied, with some spirit, “If I ever get to California, you may bet your bottom dollar that I’ll never move again.”
   
OCLC WorldCat record
Bet your bottom dollar
Author: Josef Myrow; Eddie De Lange
Publisher: New York : Triangle Music Corp., ©1946.
Edition/Format:  Musical score : Songs : English
 
Wikipedia: Tomorrow (1977 song)
“Tomorrow” is a song from the musical Annie, with music by Charles Strouse and lyrics by Martin Charnin, published in 1977.
ST Lyrics
[ANNIE]
The sun’ll come out
Tomorrow
Bet your bottom dollar
That tomorrow
There’ll be sun!