An annulment costs just the filing fees, and amounts to no more than a couple of hundred dollars in most cases. If you are in a situation that is dubious, where the reasons for annulment are not clear cut and you are denied the annulment, you can hire your own canon lawyer in the review process, which could be costly. But the basic fees for administrative costs and document production, etc. are not very high, and can be waived in cases of necessity. Compared to what people pay for a civil divorce - which can be many thousands of dollars - an annulment is practically free.
The annulment is slower than a divorce because more consideration is given to it and in addition, the Church does not wish to make annulment something perceived, like divorce, as a speedy solution to something that could possibly be resolved some other way; nonetheless, it usually takes under two years.
And the children aren’t considered bastards.
Here in PA (least Western PA) it takes about six months. Check most civil divorces and they are averaging 2.5-3 years (two years from the date of submission, you are divorced, but property division may be an ongoing issue that can last a couple more years).
To be honest I have no idea what it costs.
What I DO know is that I filed for an annulment under the hardship application for an annulment years ago. I heard nothing from the Diocese of Hartford, CT for six months until I got a letter stating that my ex-wife had filed for an annulment after I did and would I like to participate. I said I would and supplied a copy of all the documents I sent in six months earlier.
I DO know that my ex-wife's family had lots of money and had connections in the church due to financial considerations.
The annulment came through about a month later.
To this day I am convinced it was her father's money that got the annulment.