Bowser is strict, mean and somewhat rude. At times he can be truly merciless, such as when he burned his youngest son Bowser Jr in flames for not doing well in school in First episode. However, he can also be truly compassionate too, like in the end of Living with Nerdy when he sweetly forgives Bowser Jr for understanding the depth of his mistake. He is somewhat knowledgeable, but can also be very immature and snap just at the thought of something he doesn't like (like his rival Mario).
Bowser is the strongest character in the series, greatly and feared for his power by generally all characters. His most used power is his fire breath, which he uses for attacking and threatening.
Bowser's interests are not expanded upon in the series, but he seems to be sort of self-absorbed as seen in Living with Nerdy where he passionately hugs a statue of himself.