Conversational agents, such as chatbots, have increasingly found their way into many dimensions of our lives, including entertainment and education. In this exploratory study we built a child-friendly chatbot, "Ask Me Anything" (AMA), and investigated children's attitudes and trust toward AI-driven conversational agents. To prompt targeted questioning from students and drive engagement, AMA is a specialized chatbot that answers only topic--specific questions in three areas--astronomy, sneakers and shoes, and dinosaurs. We tested AMA with 63 students in a K-8 public school in the Northeast USA. Students worked in small groups, interacted with our tool for three to ten minutes, and completed a post survey. We identified three key themes that emerged from student conversational interactions with AMA: expressing wonder, surprise, and curiosity; building trust and developing confidence; and building relationships and anthropomorphizing. Also, we observed a broad attitude of openness and comfort. Students trusted the chatbot responses in general, indicating a high level of trust in and reliance on AI as a source of information. They described AMA as "knowledgeable," "smart," and that they could "trust it." To confirm their perception of reliability, some students tested the chatbot with questions to which they knew the answers. This behavior illustrated a fundamental aspect of children's cognitive development: the process of actively evaluating the credibility of sources. Our work extends and contributes to the existing body of literature that explores children's interactions with conversational agents.