Attraction between comb and paper bits

You must note that the electrostatic force equation is :

$$F = frac{kq_1q_2}{r^2}$$

The term $r^2$ matters the most.

The positive charge on the comb (let's just assume it as positive) is closer to the negative charge on the paper and farther from the positive charge on the far end of the paper.

Beacause of this separation differences the paper bit gets attracted to the comb.

Your assumption that the repulsive and attractive forces are equal in magnitude is misguiding you.
When the comb is rubbed against dry hair, elections from hair jump into the comb. This gives comb a negative charge, leaving your hairs with slightly positive charge on them. When the tiny bits of paper are brought in vicinity of the negatively charged comb, the charges on the initially neutral paper rearrange. Actually it's just the negatively charged electrons that shift a little bit towards the farther end leaving a slight positive charge on the end closer to the comb and slight negative charge is attained to the farther end (where the electrons have moved to).
The charges induced on either ends can be assumed equal if we assume no charge has escaped the paper.
Applying the expression for electrostatic force
$$F=frac{kQ_1Q_2}{r^2}$$
where k is a constant, Q₁ and Q₂ are charges on two different bodies separated by a distance r. So greater the r is, smaller is the force. Hence, the attractive force on the charges in the nearer part is greater than the repulsive force in magnitude, as k, Q₁ and Q₂ are constants.
Thus, the paper bits are attracted towards the comb.