Technically, the bear market ended today. Now personally I don't believe that this new "bull" market will hold. We will see soon enough.
The end of a bear market is only evident in hindsight. The Dow had several significant rallies during the Great Depression, but very few people would suggest that the period 1929 to 1932 was categorised by five or six short bull markets interspersed by six or seven short bear markets.
That's the difference between the long-term, or "secular" bull/bear markets and the cyclical bulls/bears that are contained within them. A secular bear market existed at least from October 1929 through about June 1932. A couple of strong rallies in the 20% range occurred on the way down. Those could be considered cyclical bulls within the longer-term down trend.
Of course it's all a matter of scale. You could take the viewpoint that the market was in a secular bear market from October 1929 until June 1949. None of the high points within that time frame came close to the 1929 high, although none of the low points after 1932 were as low. Taking this point of view, the 4 1/2 year bull market from June 1932 until January 1937 was just a cyclical bull contained within the longer term secular bear market.
Similarly, the market is often said to have been in a secular bull market from August 1982 until March 2000. A cyclical bear market occurred from August through November 1987. Using these kinds of time scales, a secular bear existed from March 2000 until March 2009, with an imbedded cyclical bull from Sept 2002 until October 2007.
Of course these are all analyses that are done in hindsight. They can't be done in real time, and thus are not actionable. Hence why long term buy and hold strategies typically outperform attempts to time the market.