As with most forums, you cannot delete your account. Read more about this particular site here: http://bmgf.bulbagarden.net/f346/how-delete-bulbagarden-account-119000/
Their official response: We don’t delete accounts ever. But we can erase posts and such and ban your account if there’s a real need for it.
Read the tip below on how to remove all your private details from your account.