Hi
Colene - I would agree with what Chuck has said in that it is better to water less often but thoroughly and preferably in the morning - as watering everyday - regardless of temperature will put your rose at risk of becoming diseased - especially as roses are prone to what is called " powdery mildew " when given excess and frequent waterings.
I also grow roses in a hot climate - similar to yours with temperatures that hover around 114 -119 Fahrenheit for months on end and have found that even with these temperatures - it is not necessary to water more than every 5 days to once a week whether the rose is established or not - but if in doubt - its always best to check the soil prior to watering.
The reason why you are not seeing an abundance of strong blooms - is because as your rose is newly planted and not yet established and is busy putting all of its strength into putting its roots down - it won't have the strength to produce strong blooms - which is why it is best to remove the buds before they bloom at this stage - as by doing this it will allow your rose to establish itself more quickly - as well as be stronger and healthier.
So at this stage - there really is nothing more to be done other than wait and providing that you remove the blooms at bud stage and don't let it entirely dry out while it is establishing itself - as well as making sure that your rose is planted in an area that receives plenty of sunlight and given a good feed with a potassium rich fertilizer - it will start thriving and producing strong blooms in next to no time