Was Bribing Hannibal’s Allies a Tactic Scipio Africanus Used to Win the War?

In terms of the Iberian tribes, it probably was. Livy mentioned that in conquering New Carthage, Scipio acquired all of Carthage’s hostages, which he promptly returned to their respective tribes, and he also acquired a lot of gold and silver. He sent most of it to Rome for their treasury, and also paid bounties to his troops, but very likely used part of it to ingratiate Spanish tribal leaders.
There is the story about the beautiful Celtiberian hostage who was brought to Scipio by his soldiers who thought he might like to bed her. She began to cry, and he asked her why she was weeping, and she told him that she wanted to marry Allucius, a prince of her tribe, and that she wanted to remain chaste for him. Her parents had come to the city with gold and silver to ransom her, and he sent for them as well as her betrothed. Scipio told Allucius that his intended bribe had been kept as safe under his charge as she would have been under her parents’ roof, and that he was pleased to return her to him for matrimony. All he requested of the young man was that he be a friend to Rome, because, after all, it was much more beneficial to be a friend to Rome that to be an enemy.
Her parents insisted that he accept the money they had brought to ransom their daughter. He had them bring it forth, and then gifted it to the young man as a wedding present. The young man was so pleased that he organized a band of 1400 horsemen to help the Roman cause.
In terms of the Numidians, Masinissa came to Scipio of his own accord, having been alienated from the Carthaginians and realizing that Scipio would eventually lead the Romans to victory over Carthage. There is a background story there too. After the Battle of Baecula, Scipio freed the Spanish prisoners but sold the African prisoners into slavery. One of the African prisoners was just a boy, perhaps fourteen or fifteen, who claimed to be of the Numidian royal house, the grandson of King Gaia and nephew of Masinissa. Scipio asked him how a boy his age happened to be on the battlefield. He admitted that his uncle had told him to stay in camp, but that he had stolen a horse and armor and rode to the battle, but the horse had spooked and thrown him, and he had been taken prisoner by the Romans. Scipio gave him gifts and had him escorted to his uncle’s camp. This may have been something that won over Masinissa. Of course, when Masinissa joined Scipio in his Africa campaign, there was a quid pro quo: Scipio gave Masinissa kingship over both his own country and the country they conquered from King Syphax who had remained allied with Carthage. Syphax himself had been bribed by Hasdrubal son of Gisco who gave his daughter, Sophonisba, to him in marriage.
Then, as now, bribery of neutral parties was all part of war, and the Carthaginians practiced it too. Scipio’s uncle Gneius Cornelius Scipio Calvus hired 20,000 Celtiberian mercenaries to participate in a campaign against the Carthaginians. Hasdrubal Barca, the younger brother of Hannibal, bribed these mercenaries to stay out of the battle. Gneius realizing that he was seriously undermanned tried to take his remaining 10,000 soldiers northward, but the forces of Hasdrubal Son of Gisco, Mago Barca and Masinissa caught up with them an annihilated most of them.
So yes, like every other competent military leader, Scipio practiced bribery and it served him very well.