Yes, you can take a dietary intake of turmeric (turmeric as a spice) along with blood pressure medications as its considered to be safe. However, it is not recommended to take supplemental dosages of turmeric/curcumin or golden paste concomitantly with blood pressure medications and a gap of 3-4 hours must be maintained.
Theoretically, it is thought that taking turmeric (high dose or supplements) along with other drugs may have an additive effect which may reduce the blood pressure significantly.
Dietary intake (turmeric as a spice) of turmeric contains much less concentration of curcumin, and thus, it may not have a profound effect.
Let us understand this better with scientific evidence.
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Turmeric Interaction with Blood Pressure Medication
1. Turmeric helps in hypertension and may not affect the working of drugs
Turmeric and its constituent curcuminoids regulate and normalise blood pressure levels.
Due to these benefits, it is highly recommended to include the natural spice turmeric in the diet. It may act as an adjuvant to other medications and therapies and may help in lowering the doses of drugs and their possible side effects.
There are hardly any studies which mention the adverse effects of consuming turmeric or curcumin with blood pressure medicines.
In a study, curcumin taken concomitantly with talinolol, a drug used for hypertension, was found to increase its absorption and plasma concentration. 
European Journal of Clinical Nutrition reports another study wherein the bioavailability of the same drug talinolol, was unexpectedly reduced when administered together with curcumin. 
Some studies have used curcumin in combination with blood pressure medicines in treating some other disorders.
Curcumin used in combination with ACE inhibitors improves cardiac function after an incident of myocardial infarction. 
Curcumin taken with a beta blocker nebivolol protects the heart from toxic effects of cancer drugs. 
These studies suggest the possibility of their use together. However, more studies are required to ascertain these facts.
Also we can’t forget that black pepper taken with turmeric regulates the absorption of other drugs as well. So if taken with blood pressure medications, it may increase their absorption and this may not be safe on long term.
Nonetheless, maintaining a gap of 3-4 hours is recommended to avoid potential interactions between turmeric and drugs.
2. Turmeric acts in the same manner as blood pressure lowering drugs
Turmeric lowers blood pressure and acts similarly to some widely used drugs such as ACE (Angiotensin Converting Enzyme) inhibitors, beta blockers and calcium channel inhibitors. 
Like beta blockers, turmeric helps in regulating heartbeat, blood flow and consequently, the blood pressure. 
It restricts calcium from entering the cells of the blood vessel and heart which relaxes the blood vessels and ensures smooth passage of blood.   Calcium channel blockers like verapamil, amlodipine, clevidipine and felodipine work in the same way. 
Turmeric is taken with black pepper to improve its bioavailability. The active component of black pepper, piperine enhances absorption of turmeric.   Being a bioenhancer, it is also known to improve drug absorption and interfere with drug metabolism.   
Thus, turmeric supplements, black pepper or golden paste taken with blood pressure drugs may have an increased therapeutic action and could lower blood pressure levels.
There are no studies conducted on this, but theoretically, it is thought that turmeric may have an additive effect on blood pressure lowering medicines and abnormally lower blood pressure.
While we wait for more research on this, it is advised to consult a doctor about this and maintain a 3-4 hour gap between taking blood pressure medicines and turmeric supplements/high dose of Golden Paste.
How to Take Turmeric / Curcumin?
There are two most popular ways you can include turmeric. One is by taking the powder (spice) and second is taking turmeric / curcumin supplements. Here are more details on both of them
Turmeric as powder
Taking turmeric powder as part of your diet is one of the best ways to take turmeric and get its benefits. If you are not used to including turmeric as a spice in your food here are two great ways to take it:
It is important to note that turmeric is poorly absorbed in the body and thus you need to take it with fats (oils) or Black pepper to enhance its absorption in the body. Golden paste does this beautifully, as it has both black pepper and oils in it.
Here is a quick article on how much turmeric you can take in a day – Turmeric dosage
If you have high blood pressure, here is a dosage guideline for you>
Turmeric powder is very safe, but It is still important to be careful while taking turmeric in certain cases, understand the precautions and possible side effects of turmeric here>
If you plan to buy turmeric powder, but confused about the brands, here is list of brands we recommend>
Turmeric / curcumin supplements
Turmeric / curcumin supplements contain, high % of curcumin, turmeric’s key active ingredients. It is helpful when you are dealing with aggressive medical conditions.
There are several types of turmeric / curcumin supplements on the market. To know more about them and best brands, refer to this comprehensive article>
Lastly, if you have used turmeric along with blood pressure medications, please share your feedback on how you took turmeric, how much, how it went and what all precautions you took. It will be invaluable for other readers.