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. “Bull market” was printed in the New York (NY) Herald on October 28, 1855.
 
The opposite of a “bull market” is a “bear market.”
 
     
Wikipedia: Market trend
Bull market
A bull market is a period of generally rising prices. The start of a bull market is marked by widespread pessimism. This point is when the “crowd” is the most “bearish”. The feeling of despondency changes to hope, “optimism”, and eventually euphoria, as the bull runs its course. This often leads the economic cycle, for example in a full recession, or earlier.
   
Investopedia
What is a Bull Market?
A bull market is the condition of a financial market of a group of securities in which prices are rising or are expected to rise. The term “bull market” is most often used to refer to the stock market but can be applied to anything that is traded, such as bonds, real estate, currencies and commodities. Because prices of securities rise and fall essentially continuously during trading, the term “bull market” is typically reserved for extended periods in which a large portion of security prices are rising. Bull markets tend to last for months or even years.
 
(Oxford English Dictionary)
bull market  n. Stock Market a market characterized by the rising price of stock, etc.
1891   Cent. Mag. Jan. 426   No office of its size in the Street made so much money for its customers in a bull market.
1931   F. L. Allen Only Yesterday xii. 301   No aspect of the campaign was more interesting than the extent to which it reflected the obsession of the American people with bull-market prosperity.
     
28 October 1855, New York (NY) Herald, “Financial and Commercial,” pg. 5, col. 1:
It would, undoubtedly, have been a bull market but for the report, soon after the opening of the first board, of two or three failures.
     
20 February 1856, New York (NY) Herald, “Financial and Commercial,” pg. 3, col. 2:
It was, in reality a bull-y market.
 
22 November 1856, United States Economist, Dry Goods Reporter, and Bank Railroad and Commercial Chronicle (New York, NY), “Money Market,” pg. 86, col. 1:
The Stock market has, consequently, been a “bull market,” but with less of buoyancy, perhaps, than for the previous week, although rates of most railroads have advanced, and stand higher than for the previous week.
   
9 October 1858, New-York (NY) Daily Tribune, “Commercial Matters,” pg. 8, col. 2:
The Stock market was decidedly a bull market today, with considerable activity in the leading fancies.
   
30 January 1860, Boston (MA) Herald, “Herald Financial Record,” pg. 4, col. 5:
There was quite a “Bull” market on the fancies, and prices rose up handsomely.
 
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
Financial—How To Make Money.A BULL market is always sensitive
Edition/Format: Article Article
Publication: Frank Leslie’s Weekly, (DECEMBER 22, 1898)
   
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
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
   
6 June 1970, The Arizona Republic (Phoenix, AZ), “Let’s take stock: Street language has its own meaning” by Don G. Campbell, pg. 37, col. 7:
As a background, then a “bull market” can be defined as a relatively long-term trend in stock prices—at least a year in duration—in which the general trend is upward.
 
11 July 1988, The Wall Street Journal (New York, NY), “An Appraisal: Money Managers Differ on the Outlook for Stocks” by Randall Smith, pg. 41, col. 3:
One reason opinions differ: There is no standard definition of a bull or bear market, as there is for a recession (two consecutive quarters of negative growth in the gross national product).
 
Ms. Garzarelli (Shearson Lehman Hutton market analyst Elaine Garzarelli—ed.) defines a bull market as a 20% rise in stock prices over at least six months.
 
25 July 1988, The Globe and Mail (Toronto, ON), “Report on Investment: Signs aplenty for the bulls and the bears” by Leonard Zehr, pg. B15:
Some analysts figure that a bull market is defined as a 20 per cent advance in stock prices over at least six months.
 
23 July 1996, The Times-Picayune (New Orleans, LA), “Strategy for taking the bull by the horns” by John Gin, pg. C1:
Depending on how you define a bull market (a 20 percent rise in stock prices), the current bull has run since October 1990, making it the second longest ever.