The terms “bull” (for rising prices) and “bear” (for falling prices) originated in the early 1700s, but the terms “bull market” and “bear market” came much later. “Bear market” was printed in the New-York (NY) Times on March 22, 1858.
 
The opposite of a “bear market” is a “bull market.”
 
       
Wikipedia: Market trend
Bear market
A bear market is a general decline in the stock market over a period of time. It is a transition from high investor optimism to widespread investor fear and pessimism. According to The Vanguard Group, “While there’s no agreed-upon definition of a bear market, one generally accepted measure is a price decline of 20% or more over at least a two-month period.”
 
A smaller decline of 10 to 20% is considered a correction. Once a market enters correction or bear market territory, it isn’t considered to have exited that territory until a new high is reached.
 
Investopedia
What Is a Bear Market?
A bear market is a condition in which securities prices fall 20% or more from recent highs amid widespread pessimism and negative investor sentiment. Typically, bear markets are associated with declines in an overall market or index like the S&P 500, but individual securities or commodities can be considered to be in a bear market if they experience a decline of 20% or more over a sustained period of time - typically two months or more.
 
(Oxford English Dictionary)
bear market  n. Stock Exchange a market characterized by the falling price of stock, etc. (see sense 8); opposed to bull market n. at bull n.1 Additions.
1903   H. I. Smith Financial Dict. 63   Bear market, a speculative term which signifies a declining market; in other words, that the tendency of prices is downward.
1926   H. J. Wolf Stud. Stock Speculation II. 25   If the above mentioned ‘bear’ will apply his remarks to a bear market, instead of a bull market, we are in agreement.
     
22 March 1858, New-York (NY) Times, “Commercial Affairs,” pg. 8, col. 3:
The character of the news was just sufficiently undecided to be construed either way on the Stock Market of Wall-Street on Saturday, and coming on what, in contrast with the buoyancy in the beginning of the present month, may be termed a Bear market, the effect was made to tell adversely upon prices.
 
24 September 1858, New-York (NY) Daily Tribune, “Commercial Matters,” pg. 8, col. 4:
The features of the Stock market are much the same as those of the last day or two. There was some irregularity of movement, but on the whole it was a bear market.
 
17 June 1869, Philadelphia (PA) Inquirer, “Financial Affairs,” pg. 7, col. 2:
So, in a universal “bull” market stocks, particularly after such a large advance in prices as that which took place during the period from February to June, are likely to tumble, for the reason that the sellers are more numerous than the buyers, and the supply becomes greater than the demand.
(...)
It is hardly probable that money can continue active throughout the summer or until the fall drain for moving the cotton and corn brings about a natural “bear” market.
   
OCLC WorldCat record
Meeting the Bear Market. How to prepare for the coming bull market.
Author: Glenn Gaywaine MUNN
Publisher: Harper & Bros.: New York & London, 1930.
Edition/Format:   Print book : English
 
OCLC WorldCat record
Common stocks as long term investments; the common stock theory tested in a bear market and remarks about its future.
Author: Donald Merrill Clayton
Publisher: 1932.
Dissertation: A.M. Brown University 1932
 
OCLC WorldCat record
The Bull and Bear Market Psychology—How It May Hurt Security Analysis
Author: Walter Gutman
Edition/Format: Article Article : English
Publication: Financial Analysts Journal, v4 n3 (194807): 15-18
Edition/Format:   Thesis/dissertation : Thesis/dissertation : Manuscript   Archival Material : English
   
Google Books
U.S. News & World Report
Volume 97, Issues 1-13  
1984
Pg. 70:
Yet, to Nurock (Robert Nurock, publisher of the Astute Investor—ed.), a bear market is characterized by a 20 percent drop in such indicators as the S&P or Dow Jones industrial indexes.
 
9 November 1987, Chicago (IL) Tribune, “Stock collapse still searching for a definition” by Pat Widder, pg. C3, col. 2:
In Barron’s Dictionary of Finance and Investment Terms, a bear market is defined somewhat vaguely as a “prolonged period of falling prices.”
(...)
Robert Stovall, president of Stovall/21st Securities, aid his parameter for a bear market is any drop in stock prices of 20 percent or more.
 
7 December 1987, Miami (FL) News, “Recent market turbulence has lessons for investors” (New York Times News Service), pg. 17M, col. 2:
Since the early 1960s there have been eight bear markets, defined as drops of 10 percent or more in stock prices, according to Christopher Caton, the director of forecasting at Data Resources Inc., the economic consulting unit of McGraw-Hill Inc.
     
18 August 1990, Los Angeles (CA) Times, “Dow Ends Down 36.64 After Late Rally Trims 63-Point Midday Loss” by Paul RIchter, pg. D4, col. 1:
“We see even further downside potential over the next weeks, and we may even go to a bear market, which we define as a 20% decline from the peak,” Louise Yamade, vice presdient and technical analyst for the Smith Barney, Harris Upham brokerage in New York.
 
4 March 1991, The Wall Street Journal (New York, NY), “U.S. Stock Analysts Mull ‘90 Slide, Looking for Clues of Future Trends” by Douglas R. Sease, pg. 26:
Technically, the 634-point drop in the Dow Jones Industrial Average between July 17 and Oct. 11—a 21% decline—satisfies many analysts’ definition of a bear market: a 20% drop in either the Dow Jones industrials or the Standard & Poor’s 500-stock index. 
 
28 May 1993, Aberdeen (SC) American News, “How high will the Dow go?” by Mark Calvey (Knight Ridder Tribune News Wire), pg. 2B, col. 1:
He (Art Bonnel, portfolio manager at MIM Stock Appreciation Fund—ed.) defines a bear market as a 15 percent to 20 percent drop in the Dow.