I have gone through this same thing for quite a number of years and will be 41 at the end of the year and have never had children or any other issues in that area. Each time i would have a smear done they would say "you shouldn't have a smear done when you are expecting your period". I would then tell them that i've finished my period or am midcycle. It would take me 3 or 4 goes of getting a successful smear done and after each consecutive go i would have to wait 3mths after each unsuccessful smear so that the cells could settle. After this entire process a whole year would virtually have gone by.
Finally i saw a dr who said this was not satisfactory and ordered a colposcopy. This procedure is quite easy, same as a regular smear only they can see your cervix much closer due to using the microscope. They dab your cervix with some vinegar which normally highlights any abnormalities which might be visible to the eye.
My problem was that even with the colposcopy i bled and this dr said that this is not normal in somebody of my age. She said a cervix would normally bleed when touched when a female has finished menopause and is on average over the age of 55 as the tissue on the cervix thins out.
They still attempted to do a smear with me, they also did a vaginal swab and in the end they took a biopsy, which is when they take a tiny bit of tissue from the cervix to have checked out as she didnt feel the smear itself would be sufficient.
This dr also said that there appeared to be some inflamation of the cervix and it can be due to a bacteria and this could be what causes the constant bleeding when touched. She then gave me a prescription for antibiotics and suggested my partner should get checked out as well. Apparently 50% of males can have a harmless type of bacteria living within the urethral opening (where they pee from) and have no side effects at all and then pass this bacteria to a female during sex. She also said that there are so many forms of bacteria out there for which there are no names for and dr's dont really know how to treat and so they will give you an antibiotic which might normally be used for certain other types of bacteria.
Anyway, that is my experience and i have to go back for them to get my results and to check whether the inflamation has cleared up which would mean the antibiotics cleared it up, otherwise she will refer me on for some other specific tests as she feels that the cercix bleeding so easily during a papsmear is definitely not right.
The other helpful thing i was told was that having your pap tests done the first week after your period is over is the best time as that is the time you have the most cells present which makes for a better determination of your results.
Best of luck and by all means dont be scared of the colposcopy, it's harmless and i wish i'd had it done LONG ago. Your health should always come first, so dont be scared, it doesnt hurt