First, if you are taking her out every four hours and she is not clean in the house you are leaving it too long. Start by taking her out every hour or so.
Take her out:
Upon waking, both from overnight sleep and after daytime naps
After every play session
After every meal
And, regularly scheduled trips outside.
Next, and this is the big issue: What do you mean by 'take her out'?
Sticking to routine is a good thing - but that routine must be appropriate to the dog's current needs and abilities. We owners have to first develop a routine that matches what the dog can do, and then once basic training is established gradually move to the routine that ultimately fits our schedules. The first days/weeks/months in a new home means that we owners have to do most of the adjusting.
It is important that the owner very clearly shows the dog what he/she is expected to do - which means being involved during those outside breaks. One can't just let the dog outside and bring him/her back in, one has to 'teach' the dog what you wish him/her to do, and reinforce the message in a positive way.
What I do - be the dog a puppy, newly adopted adolescent, adult, or senior:
Starting with once an hour regularly scheduled breaks and after sleep or meals, I put my new dog on lead and we both go out into the garden together. We start by walking the garden perimeter; when my dog starts to make the motions to go (gender dependent), I say my chosen 'piddle word' in a neutral voice. The idea is to develop an association between the action and the command. When my dog has successfully done the necessary I then offer big, excited praise and a treat. Then, only then, do I unleash my dog to play in the garden. Then back into the house. Rinse and repeat thousands of times according to the list above.
(I find a 'piddle' command invaluable, especially in Switzerland. If your dog can eliminate on command you will avoid many of the usual neighborhood disputes by first taking care of business in your garden and then continuing your walk through the neighborhoods. And, a piddle command is handy when you have to let the dog out before you catch a train...)
If my dog has an accident in the house I take him outside immediately, and go through the above process. No reaction to the accident, I simply clean it up.
If I see my dog starting to behave as if he might piddle inside, I use an 'ah!' to interrupt and immediately outside we go, using the process above.
ETA: I don't use a sharp 'No!' because mine tend to be sensitive wilting flowers - a sharp voice would be enough to link urinating=punishment in their damaged minds, causing them to try to avoid urinating at all, compounding the problem. (Some of mine come from pretty bleak backgrounds.) But one should temper the interrupter to the individual, as you know your dog's psyche best. With a happy mentally healthy pup a sharp 'No!' is fine - with a dog from a troubled background I would likely use a softer tone.
But the idea is the same - interrupt, and outside.
Key is big praise and reward when the dog urinates appropriately outside. If you are clicker training - and I strongly recommend doing so right from the beginning - the click/treat comes after the dog has finished urinating.
Some dogs catch on quickly, some take more time. Consistency is the key - and there is no substitute.
OF course, the above assumes that the dog is healthy and house training is just a question of learning/training. However, if you see any signs of straining or pain, if the urine is an unusual color, if house training takes longer than you expect it is always wise to see the vet for a check-up, bringing along a urine sample. A bladder infection will most certainly affect a pup's control.
Don't get discouraged - time, patience, clear directions, praise and reward, patience and more time will do the trick.
ETA2: Reading more carefully, it seems that your key issue is not eliminating when you want her to do so. In such a case, I would continue with frequent/hourly trips outside as above in order to more firmly establish the piddle command. Frequent repetition is the way to teach a dog - the time you put in now will be repaid a hundredfold later. Teaching a dog to piddle on command is one of the things that will make your life easier, especially if you live in a flat rather than a house with garden.