The solicitor who told you that bind over is not not a criminal conviction is a looney. Bindover is a criminal conviction, but not a serious one. It has a rehabilitation period of 12 months, or upto the date of order, whichever is longer. If you apply for naturalisation, before your sentence is "spent", then you will have to declare it and give relevant details. Caseworker may then exercise discretion, or may not.
My personal advice would be to wait until your bindover is spent, and then apply for naturalisation. This way you dont need to declare it, and a caseworker wont refuse you because you wont have any "unspent" convictions at the time of application.