Is it possible for a 3mm gap in my teeth to be filled with dental bonding?

Possible: But there are other options, including invisalign. The bonded teeth may look too big in your mouth after the space is closed. Consult with your dentist for your specific choices for treatment.

Diagnostic work: Most dentist can do a diagnostic wax up (impressions are taken, models of your teeth are made and white wax is placed onto the model teeth contoured to close the gaps) or diagnostic photography which can give you an idea of how your teeth could look

That's a lot: It's best to seek the opinion of a cosmetic dentist and an orthodontic specialist to determine what is best in your situation. If you only have the space between your upper front two teeth and you are adding 1.5 mm of bonding to the width of each tooth - you want to be assured they won't look as wide as chicklets (unusually wide).