Bleasdale, 20, who lifted her outdoor record to 4.71m at the Olympic trials, cleared 4.87m indoors in January 2012.
Yelena Isinbayeva is chasing a record third title and, although she improved her world indoor best to 5.01m, the Russian has struggled outdoors in 2012.
American champion Jennifer Suhr has the best clearance of this year at 4.83m.
Suhr, 30, who won silver behind Isinbayeva at the 2008 Beijing Games, comes into London 2012 in good form, having won the Diamond League meetings in Eugene and New York.
Brazilian Fabiana Murer, who is the reigning world champion and has a personal best of 4.85m, is also expected to challenge.
Former British record holder Kate Dennison, 28, who has a personal best of 4.61m, is also in action.
Competition starts at 10:20 BST with Bleasdale the 10th to jump. Athletes must clear 4.60m or finish in the top 12 to qualify for Monday’s final.