I am sorry to hear that your puppy Bailey is vomiting white foam, and has bloody diarrhea despite treatment with fluids and seemingly getting better for a couple days.
Vomiting foam simply is a mix of air and stomach/esophageal mucous made when she retches, it is not indicative of any disease process but tells us she is quite nauseous.
Did they check a Parvo test on her?
Did they check her for gastrointestinal parasites?
Was she put on an antibiotic?
Has she been fully vaccinated, meaning has she had more than one distemper/parvo combination vaccine with the last one being given after 12-16 weeks of age?
She is likely dehydrated because she has been vomiting, but if even water is making her vomit you need to take it away from her for now.
In most cases vomiting and diarrhea are triggered by eating something they should not, too much table food, too many treats or something they find outdoors.
More serious causes of vomiting at this age include toxin ingestions, viral or bacterial infections, a dietary allergy or sensitivity, inflammatory bowel disease, congenital internal organ failure (kidney or liver disease), or a full or partial gastrointestinal obstruction.
In a young dog, especially if she never finished her vaccine series, a viral infection such as Parvo virus, toxin ingestion, or a foreign body leading to a partial or full gastrointestinal obstruction would be the most likely cause. Given her bloody diarrhea and extreme lethargy a viral infection like Parvo virus would be very high on my list of possibilities. Secondary bacterial infections are common with Parvo virus because the virus damages the gut lining and allows infections to flourish. These can be just as deadly as the primary Parvo virus infection.
Because her symptoms have returned and seem more severe ideally she would see a veterinarian now on an emergency basis. At this stage she needs intensive care (intravenous fluids, injectable medications) that will be difficult to properly manage at home.
If that isn't possible for whatever reason there are some things we can try at home, but if she's not improving quickly she should see a veterinarian for an examination, some diagnostic testing, intravenous fluids and injectable medication to settle her stomach. At such a young age they have no reserves and this can be lethal.
To try and settle her stomach you can give either:
1) Pepcid ac (famotidine) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one quarter of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours
These are acid reducers and may help settle her stomach, stop the vomiting, get her feeling better and hopefully get her appetite back. Either one can be given for several days if necessary.
I would pick up all food for now and water for a couple hours to allow his stomach to settle after the acid reducers.
In a couple hours when you give her water make sure it is in small amounts only. If she drinks too much too quickly that can lead to vomiting. You can also offer ice cubes to lick. To get some electrolytes in you can offer a 50:50 mix of pedialyte and water.
If there is no vomiting for 6-8 hours offer a bland diet of 1/3 boiled, minced, white skinless chicken or boiled, lean hamburger and 2/3 boiled, white rice mixed with some low salt chicken or beef broth to make it easy to lap up and swallow. I recommend adding probiotics like Fortiflora, Proviable or Benebac to her meals daily to re-establish normal gut bacteria levels too.
If she refuses that you can offer a little meat baby food. If she refuses both then she needs veterinary care.
But if things go well and she does eat and doesn't vomit feed her the bland diet for 3 to 4 days then slowly start to mix back in her regular food, a little more at each meal. It should take about 5 to 7 days to slowly convert her back to her regular diet.
If she continues to vomit even with the acid reducers, runs a fever (more than 103F rectally), or has a lower then normal temperature (less then 99F), has a tense painful belly or if she refuses to eat she should see a veterinarian for an examination, diagnostics, injectable anti-nausea drugs intravenous fluids and supportive care.
Well worth checking at least a couple fresh stool samples too as parasites can cause bleeding, and their eggs/cysts are shed intermittently so they may be picked up on the second sample or third test even if the first is negative. Parasites are unlikely to be the only problem for her, but they may be a contributing factor.
Please let me know if you have any further questions.