The growing prevalence of human-AI interactions has made it essential to examine how cognitive biases shape technology acceptance. This study extends the Technology Acceptance Model (TAM) and Theory of Reasoned Action (TRA) framework by exploring how availability heuristics affect user attitudes and behavioral intentions toward AI chatbots. Through an online experiment, where participants were randomly assigned to one of three conditions: positive availability heuristics, negative availability heuristics, or a control group, this study examined whether recalling past chatbot experiences influences current perceptions and future usage intentions. Meantime, the potential moderating factor of perceived social distance was investigated. Results revealed that participants who recalled positive chatbot experiences demonstrated more favorable attitudes and stronger intentions to use chatbots in the future. However, the hypothesized moderating effect of perceived social distance was not supported by the data. These findings enhance our understanding of the cognitive mechanisms underlying TAM in human-chatbot interactions and offer valuable theoretical and practical implications for human-AI interaction design.