The Danes struck at Wareham in 876. Alfred made peace there with Guthrum, and there was an exchange of hostages. However, the Danes broke the peace and during the night they killed the hostages and left Wareham on horseback. I've seen modern references to money being paid to the Danes to sweeten the peace deal at Wareham. What primary sources show Alfred buying the Danes off in 876 or earlier?
There are two primary references that have been (and are still being) cited by early and contemporary (i.e., 18th-21st century) historians regarding King Alfred the Great paying off the Danish invaders of Wessex in 876 A.D. The two most cited references are from the 9th century: (1) Bishop Asser's "Life of King Aelfred" (Asserius de Rebus Gestis Aelfredib, written in Latin), and (2) the "Anglo-Saxon Chronicle ", originally written in Anglo-Saxon.
There are three articles in the Englsh language Wikipedia (en.wikipedia.org) that reference these two primary sources: "Alfred the Great", "Anglo-Saxon Chronicles", and "Asser".
The Wikipedia article states that the credibility of Bishop Asser's account has been in dispute by many historians over the years, including arguments that not only is the document not authentic, but also recently (1995) being declared an absolute forgery. Since Asser's original document was hand-written more than 1,500 years ago, and lost or destroyed ages ago, it exists now only in the various translated and transliterated copies that were made centuries ago,
If these two 9th century references are to be believed as being authentic and reliable, then the answer to the question being asked is clearly that King Aelfred did not pay off the Danes as legions of historians, past and present, have written. That being said, recent historians have tried to settle the historically long running disputes over many issues regarding Bishop Asser's mainly chronological account of King Aelfred's life. Some historians have agreed to disregard all previous arguments and accept Asser's account as both indisputably authentic and creditable, but others have not. The authenticity and reliability of Asser's account is then, unsettled.
However, Asser's account of King Aelfred's life makes no mention at all of King Aelfred ever having paid a bribe to any invaders of his kingdom to keep them away. An exchange of hostages, yes. But goods or money, no.
According to the Wikipedia article "Asser" (and other above listed sources), when Asser was still a Christian monk he was hand-picked by King Aelfred (a baptised Catholic) to join his court, an invitation which Asser (evidently of Welsh decent) declined to do for various reasons. Eventually, however, Asser, an anointed Catholic priest, did join Aelfred's court, but agreed to do so for only six months every year. Asser's role in Aelfred's court became one of being Aelfred's tutor, confidant, and administrator to Aelfred of the Catholic church's sacred sacraments and rites, including the sacred sacraments of Confession and Absolution, and Holy Communion with the body and blood of Christ.
Finally, in evaluating the inclusiveness of Asser's account of the life of King Aelfred, it should be noted that, as King Aelfred's Confessor as well as being his close and beloved companion, that Asser's "Life of King Aelfred" could, but certainly would not, contain anything that was revealed to him by the King while he was exercising the Catholic rite of being the King's Confessor. Consequently, Asser's account of his King's life would not include anything relating to the payment of a bribe to the Danish king Guthrum if that fact had been confessed to Asser by the King during the Catholic rite of Confession.
Two English Wikipedia articles have clickable links to on-line copies of the two primary documents historians have used to reference the Anglo-Saxon chronicles and Asser's "Life of King Aelfred", as follows:
"Anglo-Saxon Chronicle": View the clickable links in the article's "External links section for various copies of the Chronicle.
"Asser: (1) for a contemporary reference to 9th century Asser see reference to Keynes, et.al. in the article's "References section. (2) for copies of Asser's "Life of King Alfred" view the clickable links in the article's "External Links section.