Is it safe to put a bullet around the helmet?

of course not. But this is purely personal likes and dislikes.

There are rules for the US military to pin something on the helmet (hood). Its practice lasted from World War II to the Vietnam War. Especially during the Vietnam War, the things that the US military hung on the helmet were messy, and most of them were gadgets that were convenient to take in combat. The things hung by different occupations and different arms were not the same. Take the US Army and Marine Corps for example: rifleman, the most common thing is to hang one or two magazines, apply ointment to the face, and so on. Machine gunners usually bring a short bullet chain (usually no more than 2 rounds, for the last fight), mosquito repellent and so on. Grenade players wear mosquito repellent, 4mm M79 grenades and so on on their helmets.

these are because different occupations have different costumes. But generally speaking, most American soldiers in Vietnam wore mosquito repellent, playing cards of spades (representing death), amulets, cigarettes and so on. At that time, the military discipline management of the US Army was relatively strict. Their helmets were equipped with helmet cover fixing belts (belts for hanging things on helmets) and were not allowed to be smeared on them. The Marine Corps, on the other hand, is very loose in this respect. They distribute helmet covers, but they don't issue fixing straps, so many soldiers cut the inner straps into traps on their helmets to hang things. Of course, some American marines also draw messy things on their helmets, such as nicknames, anti-war slogans, slang and so on.