Probably... maybe?
I have very, very little evidence to go off of, and hopefully someone will be able to post a better answer than this.
My thinking on this is based almost entirely on the DS9 episodes Progress (season one, episode 15), Shakaar (season three, episode 24) and Bar Association (season four, episode 16). And it's still patchy.
My evidence from Progress is as basic and thin as it gets. There is a line from a ship captain that Jake and Nog are trying to bargain with:
CAPTAIN: I'll give you a hundred gross of self-sealing stem bolts. Some Bajoran ordered them from me, and now he can't pay.
Perhaps not the best evidence, given that the Bajoran couldn't pay, but would be pretty brazen to order goods physically transported via freighter without even a possibility of rendering payment. And this captain draws a distinction between paying and trading:
NOG: And they can be yours for say, five bars of gold-pressed latinum.
CAPTAIN: That's a lot of latinum.
NOG: That's a lot of yamok sauce.
CAPTAIN: Look, I'm not carrying any latinum. But I'll tell you what I'll do. I'll trade you something for it.
This is weak stuff-- but the word pay strongly suggests currency rather than barter, even though latinum itself may be a commodity rather than currency (I've never been totally clear on its role in the setting, outside of Ferengi society). But regardless of whether or not the Bajoran stem bolt orderer would have paid in latinum or some other means of exchange, it seems likely that they intended to pay in some form of currency.
This means nothing with regard to the Bajoran economy-- there's no particular reason to think that he would have necessarily been paying in Bajoran currency, if such a thing even exists. But season one takes place not too long after the occupation ended, and if the Bajoran intended to pay in money he must have gotten some negotiable currency of some kind from somewhere. Bajor is the best candidate.
In Bar Association, Quark is upset about the Bajoran Time of Cleansing (during which Bajorans fast and abstain from worldly pleasures) because it has seriously harmed his business. If we assume that Quark is telling the truth about this (which is not necessarily sound, but his bar does appear to be pretty empty), that suggests a couple of things:
- Bajorans make up a substantial portion of Quark's business
- Bajorans on Deep Space 9 have money to spend, demonstrated
by the fact that they sometimes do so at Quark's
So Bajorans must get that spending money from somewhere. They could, of course, work for non-Bajoran interests which pay them in money-- Quark's dabo girls are frequently Bajorans, and in Bar Association they are definitely working for pay. But Bajor is just getting back onto the scene in the Alpha Quadrant after the occupation, and I'm not aware of any evidence that a substantial number of Bajorans are employed in non-Bajoran enterprises. They could be bartering for Quark's services, but I don't know of any evidence for that, either.
There's even a line of dialogue suggesting that Bajorans spend money at Quark's, when Leeta reminds everyone of Quark's loss leader for dabo:
LEETA: Why don't you try your luck at dabo wheel? Remember, every Bajoran gets one free spin.
One free spin for each Bajoran (DS9 resident/worker or not). And since it's a casino game, it won't make any money off of free spins-- people have to make wagers for Quark to have a shot at profiting. And a loss leader offer is an enticement to spend money elsewhere, be it non-free spins of the wheel, food and drink, or holosuites. Therefore it stands to reason that Quark sees opportunity for profitable business with individual Bajorans, generally, suggesting that individual Bajorans have something to offer Quark for his services. The easiest generally valuable thing (to Quark) that any random Bajoran would be able to offer is some kind of money.
This argument is far from iron-clad. Bajorans come to DS9 from Bajor pretty frequently, but we don't know how much of Quark's clientele are such visitors. They could just as easily be primarily people living and working on DS9, getting money from the various interests that pass through the station in an economy largely separated from Bajor's.
But I submit that the easiest and most parsimonious conclusion is that Bajor itself has some sort of economy based around something money-like enough that it can be used reliably for routine transactions, such as eating, drinking, gambling, and enjoying holosuites, to the extent that a business' finances could depend on it.
In Shakaar, farming is a key element of the conflict driving the episode's plot. In particular there are references connecting the farming both to feeding Bajor's population as well as seemingly little coordination among autonomously governed provinces:
SHAKAAR: I don't give a damn how the rest of the galaxy looks at us. We're trying to feed our own people here and you're talking about exports.
If the farming conditions being poor (which they are, due to Cardassians poisoning farmland) could lead to a meaningful lack of food on Bajor, then Bajor has not reached the radical post-scarcity conditions which led to humanity choosing to do away with money.
That doesn't mean they need to use money, of course, but something needs to organize their society and production if scarcity is still a thing for them. In Accession (season four, episode 17) we learn that Bajorans no longer adhere to hereditary castes (which might have afforded enough social and economic organization). I can't think of any explicit descriptions of anything else which might suit those needs (which includes no evidence for money doing it!).
All quotes retrieved from chakoteya.net
Progress
Shakaar
Bar Association
