Like many canine breeds, the temperament of a dog depends a lot on how it was socialized from the time it was a puppy. I wouldn't put any child around a dog that wasn't well socialized with other people or other children. Kids have a tendency to sometimes tease or provoke a dog without even knowing they're doing so. How well a dog tolerates a behavior like this that is foreign to them depends a lot on how that dog was raised and socialized.

Bull Terriers that have been raised properly around children make wonderful pets and are as kind hearted as can be. The link below is a fantastic video which depicts hundreds of photos of nothing but Bull Terriers and the fortunite children lucky enough to grow up with one.

Bull Terriers become very attached to their owners and their families. This
usually makes them very good natural guard dogs, but care must be taken that
they are not encouraged to become possessive and jealous. While this would seem
a desirable attribute for someone who wants a dog to protect his wife and
family, it can be a nuisance if the dog does not distinguish between acceptable
strangers and malevolent ones. Bull Terriers can also become involved in the
presence of violent physical activity such as children's fist fights or
exceptionally rough play, activity where they see no reason not to join in, or
to guard the family against the physical assaults of outsiders.

Bull Terriers like to join family activity and for this reason require
constant and firm discipline. They can be wonderful with children if handled
with common sense, both by the adults and the children. Bull Terriers will
tolerate a large range of children's behavior but they will not tolerate being
teased and can be rough if constantly provoked. In their formative years, as do
children, Bull Terriers require large amounts of supervision. They are tireless
playmates and will chase balls, follow the children and watch their games for
hours on end.

Many Bull Terriers can and do enjoy the company of other dogs with certain
exceptions. Male Bull Terriers who have not been altered do not, as a rule, get
along with other male dogs. There comes a time when one of the males must
dominate, and there is inevitably an unpleasant fight after which the two must
live entirely separately for life. A male and female Bull Terrier can live
together quite happily, and two females can sometimes share the same home.
Again, care must be taken that jealousy does not arise. It is not fair to expect
an older Bull Terrier who has enjoyed the full attentions of the family to want
to share with another dog. This again is very similar to a young child who
suddenly finds himself confronted with a baby sibling - some care must be taken
to assure the older one that the youngster belongs to the whole family.
Bull
Terriers shed their coats twice a year. The loose hair can be removed by a daily
rubdown with a special rubber glove or grooming comb specifically made to gather
hair. The hair does shed during these periods and the white hairs are more
noticeable than the colored ones on furniture and clothes.

Old age brings on the usual battery of infirmities to which Bull Terriers are
not immune. A Bull Terrier may well live an active and healthy life until he is
eleven or twelve which is about the normal life span of this breed.
Males and
females vary only slightly in temperament. The unaltered males tend not to
tolerate prolonged association with other unaltered males, as previously noted.
Undesirable tendencies based on the drive can be remarkably reduced by spaying
and neutering females as well as males. There can be more difference in the
temperament of families of Bull Terriers than in general between the sexes. Some
families tend to be more possessive and less tolerant of other dogs than others,
and some families have a tendency to some shyness and apprehension with
strangers and in strange places. Some families are very bright and innovative
(which can be mixed blessing) and some are less intellectual and more placid.

Bull Terriers are unique in the spectrum of dogs. They have been carefully
selected and bred largely by responsible, caring people who understand the
legacy of their chosen breed. They can give tremendous joy or wreak havoc,
depending on the time and effort spent by their owners to control and develop
their special character.