It's possible to defend against explosive devices, but in reality you can only mitigate damage. Being aware of suspicious activity, bags left unattended, those sorts of things can be done to defend against explosives, but that can only go so far. The best we can do is be aware of our environment.
It is very hard to stop people from using explosives. Considering that simple explosives can be made using fertilizer, which anyone can go to the hardware store and buy, I do not really see it as reasonable to be able to protect against explosives. Although, we can be more cautious of suspicious people.
We can never totally defend against the use of explosives unless we are willing to surrender freedom of access, movement and public assembly. The best we can do is to exercise careful security procedures, use available technology to screen high-risk areas and limit exposure to venues that offer high value exposure.
It is nearly impossible to protect us from explosives. Women, or men, could carry a bomb in a diaper bag and casually leave it behind a bush, or in a secluded area. People don't think to look at an innocent object like a diaper bag. There are so many ways to hide a bomb, and unless you do some major searching, one can slip by the single eye.