I would echo crankarms thoughts. Iranians in Iran are different to Iranians out of Iran. Iran is led by a hard line Islamic leadership. The Revolutionary Guard certainly don't wear skirts but they way be laughing and joking with you as they tape electrodes to your intimate parts. Best avoided I'd have thought.
The vast amount of Iranian people are great people to meet, and are far from the subjective people the media like to portray. OK, the country is run by a few nutters and no more so than any other middle east country, Ok some of the rules the Government impose on the people may seem extreme for us westerners but from my own expectancies it is the only way to control a tribal country as per the whole of the Middle east. Most of the populace know where they stand regarding the rules, and understand the results if you break them.
When it comes to the lone cyclist, you will find that you would be welcomed, taken into their homes and given their hospitality, and in most cases will refuse any offer of payment. However, there are times and places where a few little monetary presents smooths the journey. But as any other country, you might well fall prey to being robbed, ripped off or some similar problem, but the chances are low, as the result for the culprits is in most cases death if caught. Hanging by craning seem the favourite at the moment!
So don,t be put off by the gloom and doom peeps, just do it, you will be surprised the amount of fellow cyclists you will meet transiting through the country both east and westwards.