Can insect repellant reduce my chances of getting infected by bacteria transmitted from a bite?

Probably not: Insect repellants are designed to prevent your being bitten by insects; they are not antibiotics or antiseptics. If you've been bitten & the site is getting redder, hurting more, swelling, producing pus, sending red streaks up the arm/leg/etc, see your doc for evaluation and treatment.

Fewer bites better : The purpose of an insect repellent is to make you less "appealing" to biting insects. They do nothing to directly limit infection transmission. But fewer stings decease your odds of being stung by an infected insect.