In recommender system research, contextual multi-armed bandits have shown promise in delivering tailored recommendations by utilizing contextual data. However, their effectiveness is often curtailed by the cold start problem, arising from the lack of initial user data. This necessitates extensive exploration to ascertain user preferences, consequently impeding the speed of learning. The advent of conversational recommendation systems offers a solution. Through these systems, the conversational contextual bandit algorithm swiftly learns user preferences for specific key-terms via interactive dialogues, thereby enhancing the learning pace. Despite these advancements, there are limitations in current methodologies. A primary issue is the suboptimal integration of data from key-term-centric dialogues and arm-level recommendations, which could otherwise expedite the learning process. Another crucial aspect is the strategic suggestion of exploratory key phrases. These phrases are essential in quickly uncovering users potential interests in various domains, thus accelerating the convergence of accurate user preference models. Addressing these challenges, the ConLinUCB framework emerges as a groundbreaking solution. It ingeniously combines feedback from both arm-level and key-term-level interactions, significantly optimizing the learning trajectory. Building upon this, the framework integrates a K-nearest neighbour (KNN) approach to refine key-term selection and arm recommendations. This integration hinges on the similarity of user preferences, further hastening the convergence of the parameter vectors.