We cannot diagnose something like a UTI on the internet. If you suspect your puppy has one, for goodness' sake, take her to the vet for a check up!
If there is no infection, keep in mind that you have a very young pup. She will urinate very frequently until she learns control, something that takes time and patience -- especially with a basset.
If there is no infection, keep in mind that you have a very young pup. She will urinate very frequently until she learns control, something that takes time and patience -- especially with a basset.