Despite significant improvements in natural language understanding models with the advent of models like BERT and XLNet, these neural-network based classifiers are vulnerable to blackbox adversarial attacks, where the attacker is only allowed to query the target model outputs. We add two more realistic restrictions on the attack methods, namely limiting the number of queries allowed (query budget) and crafting attacks that easily transfer across different pre-trained models (transferability), which render previous attack models impractical and ineffective. Here, we propose a target model agnostic adversarial attack method with a high degree of attack transferability across the attacked models. Our empirical studies show that in comparison to baseline methods, our method generates highly transferable adversarial sentences under the restriction of limited query budgets.