Question
Is there a hormone or some type of substance that I can give to my ornamental plum tree to stop it from bearing fruit?

Answer
If you want this tree to be an ornamental
flowering plum instead then spray Gibberellic acid
(Ga3) about a week after petal fall. Naphthalene acetic
acid (NAA) is a more complete chemical thinner
applied at the same flowering stage. Both the above
are growth hormones and are not considered restricted
use pesticides.
Here is an artilce on thining fruit on apples the same concept can be applied to plums but instead of thining use a heavier spray on all flowers and this should wipe our the fruit.
http://www.umass.edu/fruitadvisor/factsheets/Thinning/