Since the action already happened, you need the subjunctive "pretérito perfecto": "haya" + "participio"
I hope the puppy didn't bark too much while I was gone
Espero que el cachorro/perrito no
haya ladrado demasiado mientras yo no
estaba*.
*We use "estaba" because the event that was the barking happened during the time I was away. "Estuve" is a one-time event.
I hope the puppy didn't bother you too much
Espero que el cachorro/perrito no te
haya molestado demasiado
.
Side note: "Cachorro" is a very young dog, when they're little. If the animal has reached the adult size, we just say "perro", or "perrito" if it's small-sized.