With growing expectations to use AI-based educational technology (AI-EdTech) to improve students' learning outcomes and enrich teaching practice, teachers play a central role in the adoption of AI-EdTech in classrooms. Teachers' willingness to accept vulnerability by integrating technology into their everyday teaching practice, that is, their trust in AI-EdTech, will depend on how much they expect it to benefit them versus how many concerns it raises for them. In this study, we surveyed 508 K-12 teachers across six countries on four continents to understand which teacher characteristics shape teachers' trust in AI-EdTech, and its proposed antecedents, perceived benefits and concerns about AI-EdTech. We examined a comprehensive set of characteristics including demographic and professional characteristics (age, gender, subject, years of experience, etc.), cultural values (Hofstede's cultural dimensions), geographic locations (Brazil, Israel, Japan, Norway, Sweden, USA), and psychological factors (self-efficacy and understanding). Using multiple regression analysis, we found that teachers with higher AI-EdTech self-efficacy and AI understanding perceive more benefits, fewer concerns, and report more trust in AI-EdTech. We also found geographic and cultural differences in teachers' trust in AI-EdTech, but no demographic differences emerged based on their age, gender, or level of education. The findings provide a comprehensive, international account of factors associated with teachers' trust in AI-EdTech. Efforts to raise teachers' understanding of, and trust in AI-EdTech, while considering their cultural values are encouraged to support its adoption in K-12 education.