This study presents a cognitive trust model for travel chatbots that quantifies trust based on user perceptions of chatbot capability and intention. Analyzing feedback from 738 users of a major Indian travel platform, we find that trust formation varies significantly based on interaction frequency and success rate. Users with fewer than 10 successful interactions demonstrate the highest trust levels (0.53), while unsuccessful interactions cause substantial trust erosion, particularly among new users. Perceived desire emerges as a critical driver of trust, while the capability dimension mediates the relationship between intention and overall trust. These findings advance our understanding of cognitive trust in travel chatbots and provide practical insights for designing trust-building mechanisms in conversational interfaces for online travel booking.