Memory bloat frequently occurs in web applications. It affects system performance and may even cause out-of-memory crashes. For web applications, testers often do performance testing that repeatedly runs test scripts to reveal potential memory bloats. Under that kind of testing, without guidance to determine the running order of test scripts, time may be wasted on testing with those non-bloat-inducing scripts. To address the problem, a test script prioritisation approach is proposed for the testing of memory bloat in Java web applications. The approach predicts which test scripts are more likely to make the underlying web application exhibit memory bloat phenomena by using a learning-to-rank technique. With this prediction, the execution of test scripts can be prioritised, and the revealing of memory bloat can thereby be accelerated. The experiments on a group of web applications obtained from Github and SourceForge show that the proposed prioritisation approach is effective.