Interstitial Cystitis: This condition is characterized by chronic pain in the bladder and pelvic region, often accompanied by frequent urination and a feeling of burning or stinging while urinating. The absence of blood in the urine and a negative urine sample, combined with the patient's symptoms, make this a plausible diagnosis. The patient's history of being on POP (progestin-only pill) medication and having mild spotting could also be related to hormonal influences on the bladder.

Overactive Bladder: Symptoms such as frequent urination and urgency could suggest overactive bladder, especially if the patient experiences incontinence or a strong need to urinate.
Pelvic Inflammatory Disease (PID): Although the patient had a negative urine sample and no discharge, PID could still be considered, especially given the suprapubic pain and the fact that the patient is sexually active (implied by the use of POP medication). However, the absence of discharge and the negative urine culture make this less likely.
Irritable Bowel Syndrome (IBS): The patient's symptoms of suprapubic pain and frequent urination could be confused with IBS, especially if the pain is related to bowel movements or if there are changes in bowel habits.

Bladder Cancer: Although rare in a 34-year-old, bladder cancer can present with symptoms of frequent urination, pain, and sometimes hematuria (which is absent in this case). It's crucial to not miss this diagnosis due to its severe implications.
Kidney Stones: While the patient does not report severe, colicky pain typical of kidney stones, small stones could cause frequent urination and discomfort. The absence of blood in the urine does not rule out this diagnosis entirely.
Endometriosis: This condition can cause pelvic pain, dysuria, and other urinary symptoms, especially if endometrial implants are near the bladder or ureters. The patient's history of mild spotting and use of POP medication could be relevant.

Bladder Endometriosis: A specific type of endometriosis where endometrial tissue grows into the bladder wall, causing cyclical symptoms related to menstruation, including pain and urinary frequency.
Eosinophilic Cystitis: A rare condition characterized by an eosinophilic infiltration of the bladder wall, leading to symptoms similar to interstitial cystitis.
Tuberculosis of the Urinary Tract: Although rare in many parts of the world, TB can affect the urinary tract and cause chronic pain, frequent urination, and other symptoms similar to those presented by the patient.

Given the differential diagnoses, the next steps could include:

Further questioning about the patient's symptoms, including the timing and severity of pain, and any factors that exacerbate or relieve symptoms.
A physical exam, including a pelvic exam, to assess for tenderness or other abnormalities.
Additional diagnostic tests such as urinalysis for cytology (to rule out bladder cancer), ultrasound of the kidneys and bladder, or cystoscopy to visualize the inside of the bladder.
Consideration of a trial of medications for overactive bladder or interstitial cystitis, depending on the suspected diagnosis.
Referral to a specialist (urologist or gynecologist) for further evaluation and management.