Series Circuits are characterized by a single pathway from the + to the - terminal of the battery. The bulbs are arranged in a consecutive fashion such that any charge that passes through the first bulb will also pass through the second and the third bulb. Each bulb offers a resistance to charge flow. And since charge passes through every bulb, more bulbs result in more overall circuit resistance. In fact, the overall resistance of a series circuit is equal to the sum of the resistance values of the individual resistors (bulbs).
Parallel circuits are quite different because the bulbs are all placed in an individual branch with each branch operating independent of the others. It is analogous to toll booths on a tollway. While each toll booth offers resistance to the flow of cars, placing each toll booth in its own lane (or branch) means that having more toll booth lanes will reduce the overall resistance and increase the flow of cars through the toll area. For circuits, it works similarly. Adding more bulbs will also add more branches (lanes) and decrease the overall resistance while increasing the flow rate or current. So two bulbs, each in its own branch, will be less resistance than any of the individual bulbs. And three bulbs, each in its own branch, would be less resistance than any two of the bulbs or even any one of the bulbs. And as such it is reasonable that the overall resistance will always be less than the resistance of any of the indivudal bulbs.