Encounters with grizzly bears were very common in the mountains of the West. The journals are full of close calls, maulings, deaths, and hunts for these animals. Most of the hunts are, shall we say, exciting. Here is an excerpt from Osborne Russll's journal about a chance bear hunt:

I sat down upon a rock which overlooked the country below me at length casting a glance along the
South side of the Mountain I discovered a large Grizzly bear sitting at the mouth of its den I
approached within about 180 paces shot and missed it. he looked round and crept slowly into his
den I reloaded my rifle went up to the hole and threw down a stone weighing 5 or 6 lbs which
soon rattled to the bottom and I heard no more I then rolled a stone weighing 3 or 400 lbs into
the den stepped back two or three steps and prepared myself for the out come. The Stone had
scarcely reached the bottom when the Bear came rushing out with his mouth wide open and was
on the point of making a spring at me when I pulled trigger and Shot him thro. the left shoulder
which sent him rolling down the Mountain It being near night I butchered him and left the Meat
lying and returned to Camp. The next day I took the meat to camp where we salted and smoked it
ready for winters use.

A.J. Miller's "Narrow Escape from a Grizzly Bear". This was a field sketch, not the finished painting.

More like titanium stones

I think I might have a grizz story that beats that:

I believe it was the Lt. Wilkes party that was headed south on the Hudson Bay trail to California in 1841 In the mountains in southern Oregon they encountered a grizzly and shot it. The wounded bear ran off into a dense patch of pucker brush. One of the trappers commented to a local Indian that was traveling with the group that if he wasn’t such a woman he would go in there and finish that bear. The Indian stripped off his shirt asked for a knife and a hatchet and went in after it. There was a sudden thrashing, terrible growls and blood curdling screams from the brush and a minute later the Indian staggered out of there mortally wounded, dying shortly after.

So many good ones about bears BP, this one is long, but most likely my favorite, from River of the West:

On one of these hunting expeditions that winter, the party consisting of Meek, Hawkins, Doughty,
and Antoine Claymore, they had been out nearly a fortnight without killing anything of consequence,
and had clambered up the side of the mountains on the frozen snow, in hopes of finding
some mountain sheep. As they traveled along under a projecting ledge of rocks, they came to a
place where there were the impressions in the snow of enormous grizzly bear feet. Close by was
an opening in the rocks, revealing a cavern, and to this the tracks in the snow conducted. Evidently
the creature had come out of its winter den, and made just one circuit back again. At these
signs of game the hunters hesitated--certain it was there, but doubtful how to obtain it.
At length Doughty proposed to get up on the rocks above the mouth of the cavern and shoot the
bear as he came out, if somebody would go in and dislodge him.
“I’m your man,” answered Meek.
“And I too,” said Claymore.
“I’ll be d_d if we are not as brave as you are,” said Hawkins, as he prepared to follow.
On entering the cave, which was sixteen or twenty feet square, and high enough to stand erect
in, instead of one, three bears were discovered. They were standing, the largest one in the middle,
with their eyes staring at the entrance, but quite quiet, greeting the hunters only with a low growl.
Finding that there was a bear apiece to be disposed of, the hunters kept close to the wall, and out
of the stream of light from the entrance, while they advanced a little way, cautiously, towards their
game, which, however, seemed to take no notice of them. After maneuvering a few minutes to get
nearer, Meek finally struck the large bear on the head with his wiping-stick, when it immediately
moved off and ran out of the cave. As it came out, Doughty shot, but only wounded it, and it came
rushing back, snorting, and running around in a circle, till the well directed shots from all three
killed it on the spot. Two more bears now remained to be disposed of!
The successful shot put Hawkins in high spirits. He began to hello and laugh, dancing around,
and with the others striking the next largest bear to make him run out, which he soon did, and
was shot by Doughty. By this time their guns were reloaded, the men growing more and more
elated, and Hawkins declaring they were “all Daniels in the lions’ den, and no mistake.” This, and
similar expressions, he constantly vociferated, while they drove out the third and smallest bear. As
it reached the cave’s mouth, three simultaneous shots put an end to the last one, when Hawkins’
excitement knew no bounds. “Daniel was a humbug,” said he. “Daniel in the lions’ den! Of course
it was winter, and the lions were sucking their paws! Tell me no more of Daniel’s exploits. We are
as good Daniels as he ever dared to be. Hurrah for these Daniels! “ With these expressions, and
playing many antics by way of rejoicing, the delighted Hawkins finally danced himself out of his “
lion’s den,” and set to work with the others to prepare for a return to camp.

I have always loved that one too. One of the reasons Joe Meek would be one heck of a movie.

I also loved the story about the time Joe and another trapper hid under their blanket when a grizzly walked unexpectedly into camp. The bear walked all over the blanket and men while they dared not make a sound. This went on for quite a while and finally the bear became bored and walked away. Joe and the other trapper hunted it down, killed it, and after it was dead Joe got up on the bear and walked all over it prostate body.... "So it could know what that felt like to be trampled like that".