I know female tourists from most countries -- single or married -- are eligible for Iran visa. could this be true?
The solo female travelers are eligible to get an Iran visa. So being a solo traveler as a female makes no problem, the reason of the rejection may be something else.
For Iran visa you should fill in the visa form on Iran visa application, it takes about 10 working days to get your reference number and two working days to collect your visa at the embassy by direct referral or one working week by posting the docs to the embassy. You can pay the visa fee in cash in Iran.
Check the cheapest Iran tours.