In most Western countries, adult bridesmaids pay for their own bridesmaid dresses. If the adult bridesmaids are still financially dependent on their parents, as college students often are, their parents do as your parents did, and pick up the bill. Parents of child attendants similarly buy the outfits for the children.
Bridesmaid dresses should match bridal wedding dress. There are countries where this rule is not followed -- South Africa comes to mind -- but if you lived in such a country, someone would have offered to buy you a bridesmaid dress by now! If your problem bridesmaid comes from another country, or is part of a close-knit, traditional family of foreign origins, it's possible that she is only aware of her own people's customs. Try explaining tactfully that the local custom is different from what she's used to, and that you had no intention to offend.
There are, of course, other reasons a bridesmaid could balk. First, she may regret agreeing to be a bridesmaid, so refusing to pay for her own dress is a convenient reason to resign. If she is a distant acquaintance chosen so that your bridesmaids would match a specific number of ushers, a relative included as a duty, or a formerly close friend that hasn't seemed so close in recent years, there's a very good chance that she just doesn't want to participate. Her absence from the wedding party will be no loss, and no one will think twice about any uneven numbers that may result.
Second, she may be unable to afford the dress, but embarrassed to say so. Bridesmaid dresses run about double the cost of a comparable evening gown. If you're accustomed to wearing well-made clothes in fashionable cuts and subtle colors, you may gravitate to bridesmaid dresses that have a $300 price tag. That's chump change compared to the cost of a formal wedding gown, but it's much of a month's rent to a bridesmaid who is just out of college, trying to pay college loans out of her tiny first-job paycheck, and unwilling to ask her parents for help.
Third, she may hate the dress you've chosen. Even best friends ordinarily do not dress alike, which should give us all a clue about the difficulty of choosing an expensive dress that will please three to six women who may or may not be friends. If your problem bridesmaid's figure is the least bit unusual, the dress may hate her too.