The flag was not used at the time, or at any time, to march under, or for any other purpose,–had no political significance whatever. It was not recognized as having been adopted or used for any political purpose or adopted by any authority whatever. I doubt whether Fremont ever saw it. There never was a “bear-flag party,”–known as such party at the time.
(John Bidwell. “The Bear Flag: More Light on an Historic Incident.” Overland Monthly, May 1895. This article can be viewed at the University of Michigan archive, http://quod.lib.umich.edu/m/moajrnl/)
John Bidwell had a decidedly low opinion of the “Bears.” As far as he was concerned, they were a shiftless bunch of hunters and trappers, incited by Fremont into starting a war for which their was no justification. Bidwell was convinced that California would come under American rule by peaceful means eventually, and that there was no reason or authority for Fremont to start a war. As he told Rockwell Hunt, “If there every was an unjust war in this world, it was that war. It was an unjustifiable war.”
As for the flag:
The bear flag was left at Sonoma. Neither did we march under the bear flag at any time, nor under the American flag, or any flag, till we arrived at Monterey and found the American flag flying there, and organized the California Battalion of Mounted Rifleman, and Fremont was made lieutenant-colonel in command by Commodore Stockton, who brought the first authentic news of the war with Mexico. And there we raised, and for the first time, the American flag.
The bear flag was eventually donated to the Society of California Pioneers, who displayed in their Pioneer Hall. It was destroyed in the fire that followed the San Francisco earthquake of April 1906. A replica hangs in the Sonoma Barracks, at Sonoma State Historic Park.
For more about Bidwell and the Bear Flag, see also https://nancyleek.wordpress.com/2014/12/12/the-bear-flag-story/