No worries...just because its rainy season, it doesn't mean its gonna rain everyday...nor will all vehicular traffic cease for the season...
You're in a car, so you'll be ok...the Peugeot bush taxis do fine as will you...if you happen to be off road and you come upon a suspicious patch of road or potentially deep puddle...stop, walk ahead, and take a peek.
Other than that you should be fine. I lived in the Tambacounda area for a couple years as a Peace Corps volunteer and have travelled through Mali, Senegal etc...you'll be ok...how is your French though?
And if you find yourself en brousse in a pinch ask for a Volontaire-Toubab...Corps de la Paix Americain...they're the only white people around that will speak the local language...and will help you out.