Boromir was the first son of the Steward of Gondor and a captain of Gondor. Yet, he was sent without escort North-West with only his horse, shield, sword, and horn to investigate Faramir's dream. Why didn't Denethor send some soldiers with him, or perhaps a guide? The chances of him being injured, lost, or waylaid seemed pretty high given that he didn't even know where Rivendell was.
The only indication we get for why he went alone is because the way was
"full of doubt and danger..."
Boromir wouldn't allow his brother to go, because of the above fears, and decided he would go himself. His father likely demanded he take people with him but Boromir would've had the same fears for them as he did for his brother.
Therefore my brother, seeing how desperate was our need, was eager to heed the dream and seek for Imladris; but since the way was full of doubt and danger, I took the journey upon myself. Loth was my father to give me leave, and long have I wandered by roads forgotten, seeking the house of Elrond, of which many had heard, but few knew where it lay.’
Fellowship of the Ring - Book II, Chapter 2: The Council of Elrond
Another reason, may be because the people of Gondor expected no dangers to their West. As Boromir says, they've protected the West from the dangers to the East.
By our valour the wild folk of the East are still restrained, and the terror of Morgul kept at bay; and thus alone are peace and freedom maintained in the lands behind us, bulwark of the West.
Denethor and Boromir likely would not have feared what lay West given the horrors they faced to the East.
Boromir described the lands to the West as being protected and "behind" the fighting:
But still we fight on, holding all the west shores of Anduin; and those who shelter behind us give us praise, if ever they hear our name: much praise but little help. Only from Rohan now will any men ride to us when we call.
There is but one note made about the journey outside of the trilogy and it reinforces the bravery of Boromir to travel on his own. This, in my opinion, strengthens the idea that Boromir did not care to put other people at risk but himself, knowing the effect their losses would be on the wars to come.
When Boromir made his great journey from Gondor to Rivendell — the courage and hardihood required is not fully recognized in the narrative — the North-South Road no longer existed except for the crumbling remains of the causeways, by which a hazardous approach to Tharbad might be achieved, only to find ruins on dwindling mounds, and a dangerous ford formed by the ruins of the bridge, impassable if the river had not been there slow and shallow — but wide.
Unfinished Tales, Part 2, Chapter 4, Appendix D, The History of Galadriel and Celeborn: The Port of Lond Daer