Being married or single is a life-style choice.
It's probably more approriate to use the words "attached" and "free" However relationship status is also a state of mind.
Two people who live together but are NOT married may not consider themselves to be "single" while another couple may be "legally married" but have living separate lives or even apart for years.
I believe the term "single parent" in this day and age has nothing to do with marital status. It simply means that individual is primarily responsible for taking care of the child's needs.
Using the label of "bastard" is seen as giving the innocent child a negative name. He/she shouldn't be looked at differently because of the actions of their parents. Oddly enough a lot of "pro-life" people are the one's who want to OSTRACIZE the child with that label. On the one hand they applaud the woman for "choosing life" and on the other hand they look down upon her and the child. Although it "takes two" to conceive legally (only the woman can "choose" whether or not a birth takes place.)
Lastly more and more women are choosing to have children without marriage. Actress Halle Berry, Madonna's first child, just to name a couple of famous people. No one is calling their children "bastards". We are also seeing single women like Sandra Bullock adopt children. This would make a her a "single parent".
There are also single women that visit sperm banks to conceive. Should we consider their off-spring to be "bastards"? or is that only reserved for kids where the mother knows whose seed impregnated her? Being a Godparent or following the death of a family member could task a person with the responsibilities of being a "single parent"
When it's all said and done whatever a person considers themself to be is "their choice". Most people could care less. One man's opinion! :-)