The British no 1 was unable to clear 4.65m as Cuba’s Yarisley Silva taking gold with a jump of 4.70m – the lowest winning jump in a worldwide championships since 2010.
Bleasdale failed twice at her opening height of 4.45m, but the reigning European indoor champion cleared it at the final attempt and then 4.55m at the first.
The Sky Academy Sports Scholar missed the World Championships in Moscow last year due to injury but had performed well this season, achieving three clearances of 4.71m or higher.
"I'm really, really gutted," she said. "I felt great coming in and had the most amazing warm up but it was just not my day. I need to look back with my coach and see what happened.
"I'm really frustrated and really upset. I felt like I had been on a long road back from my injury to come here and perform and it's not gone well. But I'll learn from it and improve as I always do.
"We all have setbacks and this is a big one for me but the Commonwealths and Europeans are coming up outdoors - they're really big Games for me and I really want to get things right and do well there."