Each atom has a different atomic radius, which is defined as the distance from the nucleus to the outermost electrons.
As the number of electrons increase across the rows, the atomic radius becomes smaller because there is a stronger magnetic pull between the nucleus and the electrons.
Since it is the outermost electrons that engage in bonding, the length of the bond depends on electrons in atom A and atom B coming close enough together that their outermost orbitals overlap.
Think of it this way, if you have a basketball and a tennis ball and touch them together, the distance between their centers could be called the covalent bond length. But if you compare basketball/tennis ball to beach ball/basketball "covalent bond", you can see that the larger the atoms, the longer the distance between their centers, and therefore the longer the bond length.
Hope this helps.
