Proposed by Robert W. Bussard in 1960, and later featured in the works of Larry Niven and Poul Anderson, which novel or short story was the first to utilize a Bussard Ramjet?
@DVK's answer clearly has earlier stories, but it is not entirely clear that they are SciFi or addressing Bussard Ramjets - so despite being in the question, I am going to put forward the case for Larry Niven.
The earliest reference I can find is in 1966, in the in the short story The Warriors. In this story the "Angels Pencil" is a fusion powered human colony ship. The alien Kzinti telepath reports on the design of this ship:
"They use an electromagnetic ramscoop to get their own hydrogen from space"
The most detailed description of Bussard Ramjets from Niven is in the short story "The Ethics Of Madness", from 1967. Here the ramjet technology is clearly described, and the protagonist in the story is the designer of the 'Safe Ramjet' ship that is core to the plot.
Niven references the technology widely in subsequent short stories and Novels including Ringworld, Ringworld Engineers, A Gift from Earth & Protector, the latter describing a battle between ramjet ships that takes months or even years to complete.
The novel of his story World of Ptavvs (1968) also includes description of Ramrobots - the automated ramjet powered ships that both explored habitable planets, and refueled and re-supplied the colonists who travel by 'slowboats' to the colonies. However I cannot find a copy of the earlier short story of the same name from 1965 to confirm that it has the same detail about ramjets.
I guess this can't be a "Bussard" ramjet because it's from before 1960 (1941 in fact), but it seems like the same general idea, or at least close enough for science fiction. I'm referring to Robert Heinlein's novel Methuselah's Children, originally published as a serial in Astounding Science-Fiction. The following extract is from Part II, on p. 84 of the August 1941 issue (available at the Internet Archive):
To be sure, many of the naval craft he was trying to outrun could accelerate higher than two gravities, and their crews could stand up physically under much more for short periods. But a naval vessel's period of high acceleration was strictly limited by her fuel tanks.
The New Frontiers had no fuel tanks; she "lived off the country," gathering up any mass that lay in her path with a sweep field—meteors, cosmic dust, stray atoms. If the "country" was "poor" in stray matter, any mass from within the ship was fuel for her hungry converter—furniture, clothing, food, even dead bodies. The converter accepted them all—mass was energy; energy, mass. Each tortured gram, in dying, gave up nine hundred million trillion ergs.
I think Sullivan's "We Are Not Alone" (1964) may qualify, though it kind of straddles the line between popular science and SciFi.
Another possibility the same article mentions is 1964 Stephen Dole’s RAND Corporation study Habitable Planets for Man which was released as a popular title called, simply, Planets for Man, co-written with Isaac Asimov. But it doesn't sound like it elaborated on propulsion in enough detail to be sure it referred specifically to Bussard Ramjets.