You’re eligible to apply:
Who You Are:
• You are a citizen or eligible national of a Visa Waiver Program country.
• You are currently not in possession of a visitor's visa.
• Your travel is for 90 days or less.
• You plan to travel to the United States for business or pleasure.
• You want to apply for a new authorization for one person or a group of applications for two or more persons.
What You Need:
• Valid passport from a Visa Waiver Program country.
• Valid credit card (MasterCard, VISA, American Express, and Discover (JCB, Diners Club)) or PayPal to pay the US $14 per application.
• Your contact information.
• Your most recent employment information, if applicable.
Source: ESTA Requirements
Eligibility for an ESTA doesn’t require a clear admission record. Now you of course have to honestly answer the question about whether you’ve ever had a visa denied. But given that you’ve had successive B visas, perhaps your ESTA application will be successful.
Let us know!