Does having pups affect the timing of a bitches following seasons?

Sometimes. Some dogs come in the same time as expected, others are early and many are late....

My last girl was late (by about 2 months) the first litter and then on time as expected, the second litter.

Thank you, I will stop worrying about it now.

In my own bitches they have usually been 4 - 8 weeks later than if they had not had puppies.

It can vary enormously - one of my girls had a litter last October.  The other girls came in in March and I expected her too.  Here we are in August and still no signs...  Her previous litter was very successful and I want to repeat and keep a bitch puppy - do I mate when she does come into season or wait until  the following one - possibly over a year away?

There's nothing wrong with mating her when she comes into season (except for all the coronavirus crap to deal with).