Bondage and blood thinners is not a topic that's likely to come up with too much frequency, but it's a very important issue to be aware of and one that we've been asked about often.
I prefer starting with "what medications do you take?" rather than "do you have any medical problems?" when I am asking questions to get health information from a potential bondage bottom. I find that asking about medications gets better and more specific information, because many people answer the question of whether they have medical problems with a knee-jerk "nope!" When you ask this question, you will often want to follow up with asking WHY the person takes a given medication (many have multiple indications and I wouldn't assume a given diagnosis). If you're not sure what implications a given medication has for bondage, I would always err on the side of caution and ask the person to consult their doctor. Being honest with your medical professionals is always best, but if the bottom feels they can't ask their doctor directly about bondage, they might ask whether they are healthy enough for yoga (including inversions) and rock climbing.
This article is intended to specifically discuss what happens when your health questions result in a disclosure that the person you'll be tying up is on blood thinning medications. Medications like ibuprofen, naproxen, and aspirin are relatively mild blood thinners. These medications fall into the NSAID (nonsteroidal anti-inflammatory drug) category. Note that tylenol (acetaminophen) is NOT a blood thinner. If someone is taking these medications, the most important question is WHY- the meds themselves are not an exclusion for any sort of bondage, but if they tell you they're taking the ibuprofen because they recently sprained their ankle, that might change your bondage plans. Another example of a relatively mild blood thinner is plavix (clopidogrel). This medication is usually given after someone has a heart attack and has cardiac stents placed- while the medication itself isn't a contraindication for bondage, I would want to know why they're taking it and if they've been cleared by their doctor for strenuous activity.
Now we move into heavy duty blood thinners. These medications include warfarin (coumadin), lovenox, and pradaxa, and they are nothing to fuck with. When you're on these medications, any trauma that might otherwise be negligible can be VERY serious, even fatal. A relatively minor impact to the head can cause a brain bleed. When patients go on these meds, they are generally advised by their doctor to avoid any risky activity (such as riding motorcycles or downhill skiing) for as long as they are taking them. Avoiding all "contact sports" is pretty standard advice [1]. And again, you also want to consider WHY the person is taking this medication, as reasons may vary from heart arrhythmias to valve surgery to pulmonary embolis to DVT, and these conditions independently have implications for bondage.
I would be very conservative in doing floorwork with someone on potent blood thinners. I would want to use thick, soft bondage material (this may be a time to break out the scarves instead of rope), have the bottom in a lying position (not standing where there is risk for falls), monitor them even more closely than usual, plan a scene that does NOT involve them struggling (which can cause trauma and affect bondage tightness/position in unexpected ways), and in general make the bondage "fluffy" and not strenuous. Only work within your own comfort level, and really keep in mind that these are serious medications.
Moving into suspension- there are a few different aspects to this. One is that any fall would likely have catastrophic consequences for someone on blood thinners, so your suspension stakes are higher in that way. Of course ideally we would never drop someone (ideally you wouldn't crash your motorcycle either) but with blood thinners the stakes are just SO high. Minor trauma that almost anyone else would walk away from could fairly easily kill someone on blood thinners.
Another aspect is that of course rope can cause bruising, and anything that causes bruises is going to cause bruises many times worse if the person is on blood thinners. I would worry about forming large hematomas. The sensitivity to trauma is just so high. Add this to the fact that maintaining a therapeutic range on coumadin is very tricky... Unless the bottom had their levels checked that day, I wouldn't ever trust that someone was in the therapeutic range, which means they could easily be extremely hyper-anticoagulated and VERY high risk for extreme bleeding/bruising with even very minor trauma... and you'd have no way to identify that.
Then to reiterate, there's the question of WHY they're on the blood thinner to begin with, because there's gotta be a real good reason... Some wouldn't themselves be terribly relevant to suspension (a pulmonary embolism 4 months ago) but some very much would be (heart arrhythmia, artificial valve, etc).
My personal risk assessment is that I would not suspend someone who was on potent blood thinners. I wouldn't say this is the decision that is right for everyone- do your research, gather as much information as possible, and make an informed decision.
References:
[1] A Patient's Guide to Taking Blood Warfarin, American Heart Association
http://www.heart.org/HEARTORG/Conditions/Arrhythmia/PreventionTreatmentofArrhythmia/A-Patients-Guide-to-Taking-Warfarin_UCM_444996_Article.jsp