Twitter bot detection has become an important and challenging task to combat misinformation and protect the integrity of the online discourse. State-of-the-art approaches generally leverage the topological structure of the Twittersphere, while they neglect the heterogeneity of relations and influence among users. In this paper, we propose a novel bot detection framework to alleviate this problem, which leverages the topological structure of user-formed heterogeneous graphs and models varying influence intensity between users. Specifically, we construct a heterogeneous information network with users as nodes and diversified relations as edges. We then propose relational graph transformers to model heterogeneous influence between users and learn node representations. Finally, we use semantic attention networks to aggregate messages across users and relations and conduct heterogeneity-aware Twitter bot detection. Extensive experiments demonstrate that our proposal outperforms state-of-the-art methods on a comprehensive Twitter bot detection benchmark. Additional studies also bear out the effectiveness of our proposed relational graph transformers, semantic attention networks and the graph-based approach in general.