It's too difficult and too dangerous diagnosing a child with bipolar disorder. Bipolars are frequently mis-diagnosed with ADHD and schizophrenia cos the behavior resembles each other somewhat.
Children will be "manic" and act out, it's natural.

But having been a child once myself, and since my disorder was triggered very early (age 7-8); I had my first suicide attempt at age 9, and my first manic episode at age 11-12. No one picked up on it though, and I managed to cope with my disorder for years until I was diagnosed at age 16. I was lucky to get diagnosed so early, cos it's been one heck of a ride since then.

My previous diagnoses, from age 13 to 16, were: winter depression, teenage depression, depression and then dissociation and theories about PTSD. It's hard to diagnose BD in general, and when you're dealing with a child or a teenager it's even harder - cos they act "bipolar" anyway.

PS. I got my diagnosis because I overdosed on (20) rohypnol, (30) sobril - with a jägermeister chaser... because I was bored. Typical mania. I was sent to the isolation at a psychiatric ward where they kept trying to make me say that I was suicidal, which I wasn't, and that's when a little light bulb lit up for the psychiatrist.
Never mind that I had been suicidal, self injuring, being promiscuous and doing drugs, stealing/shoplifting etc for years - it took a drug overdose to get diagnosed. Before you go really overboard with your behavior, to the doctors you might as well be suffering from borderline, schizophrenia, adhd, or a dozen other disorders. That's why it's so hard to get the diagnosis right.