If you're cycling through Iran, you should first decide which direction you want to go. After all it's a big country and there's no shame catching a few buses and trains to make the most of your trip through Persia.
Some Bus Tips and Challenges
#1 - Iranian bus drivers are notoriously in a rush and not overly friendly.
#2 - Your bike is going underneath the bus, which means it will get bashed around and dirty. So try to secure it the best you can.
#3 - The drivers will often charge you for putting your bike on the bus, even if it's virtually empty. In my experience they'll demand about US $10, but this may depend on the driver or bus line. They may also try to sting you when you arrive at your destination, rather than allowing you to negotiate before you buy the ticket. Just try to stay firm on the $10 before you put your bike on the bus.
#4 - Bus tickets are generally about US $8-12 between most cities such as Tehran to Kashan to Esfahan to Yazd and Shiraz. But long distance buses between say Tehran and Bandar Abbas is going to cost upwards of US $30. In which case you're probably better off catching a train that has fold down beds.
Train Tips and Challenges
#1 - The train is another option, especially for long distances if you're traveling with friends. Trains generally have seating or bed berthers with either 2, 4 or 6 bed cabins coming with snacks, pillows and clean linen. 2nd class train tickets usually cost similar as their bus equivalents if seating only. First-class tickets are easier to obtain but cost over double the price of a bus ticket to the same destination. There is a restaurant carriage on the train, plus carriages for different classes.
#2 - Train tickets are more limited than bus tickets and tend to sell out before the day of travel. Be especially careful during weather disruption or public holidays (it feels public holidays fall every other week in Iran). So try to buy your ticket at the train station ahead of time, and notify them about your bike when you purchase. Travel agencies, hotels and locals can also help with the booking process. Just be careful about commissions, better agencies can match the counter price, but hotels and locals might charge higher.
#3 - Your bike must be checked as cargo for about $5-10 extra.