Haven't been to Iran but *have* been to Afghanistan.
Take two very large pieces of very light fabric -- what's called a "wax" in Africa. When you get off your bike, you wrap one very loosely around your waste as a skirt over your bike pants (tightly, waxes make really attractive travel skirts outside of Iran, FYI), and use the other as a head scarf and upper body covering. I second the recommendation for one of those tubey head scarf thingies (in fact, take two, in case you lose one). Your helmet will fit over it easily, and when you take your helmet off, make sure your hair is hidden under the tubey head scarf thingy, and then throw over your second wax on your head (
like this), you will meet most Iranian cover requirements. You can get waxes at most import clothing stores, "hippy" type stores, Indian and Pakistani-import stores, etc.
For off-the-bike touring, have a look in the women-of-a-certain-size section of your local department store -- I found great light weight, long-sleeved, LONG shirts that I wore in Afghanistan over t-shirts, long-sleeved tight shirts or long underwear. They top needs to go WELL past your butt and your crotch. With the head tube thingy and the wax as a head scarf over that and my upper body, I had no problems.
If there are any Indian or Pakistani-owned shops near you (many really large cities in the USA have such), look for a men's shalwar kameez -- the top makes an EXCELLENT women's top in a country requiring maximum coverage (outside of a full body hijab or burqa).
The keys are:
-- cover all skin
-- cover your hair
-- cover your figure
-- cover your butt
Actually, that last one is always important for me.