Here's a brief(?) overview of currency and banking relevant to your system.
There's two basic types of currency. Fiat money, in which the money has no intrinsic value but people accept it as legal tender. Almost all money today is fiat money. It's very convenient, and it's universally accepted. Its value can be indirectly controlled by adding or removing currency from the economy. The amount of currency can be expanded along with an expanding economy avoiding deflation. The disadvantage is poor fiscal policy can devalue your money, sometimes beyond worthless.
Commodity money is when the money itself has value. It can be a valuable item which becomes accepted as a standard-ish form of currency: in a pioneering society this might be livestock, steel blades, alcohol, candy... anything that was a needed commodity and came in fairly standard units. Or it can be coins made of precious material minted by an authority. The advantage is it always holds some value. The disadvantage is that value will fluctuate with the market and region. It can be very inconvenient to carry. People might not accept your money if they don't need, say, chickens... but coins will always be accepted. And the amount of currency cannot easily be controlled by a central bank to regulate inflation and deflation, even with coins you only have so much precious metal.
Representative money is like a combination of commodity money and fiat money. Instead of carrying around a chicken you carry around an IOU redeemable with some authority (a bank or government) for a chicken. Its value lies in both the value of the chicken, and the trust that the authority will give you your chicken should you ask for it. Representative money effectively operates as fiat money with the option of cashing it in in case the value of the money drops. It's intended to limit the amount of money which can be printed to control inflation. US silver certificates were representative money.
What you're proposing is, essentially, commodity money. They're equivalent to minting coins out of precious metals. You can exchange them for goods and services, or you can "melt" them down to use as material for doing work. Replace "magic" with "fuel" or "electricity" and you see how there's a generic utility to the commodity.
However, the bit and clip itself is worthless. It has to be charged and can only be charged by authorities. You are effectively creating prepaid debit cards, but backed by commodities rather than fiat. Once charged, the magic can be transferred between clips, presumably in increments, without the authority. Unlike a prepaid debit card, it can be "melted down" and used directly like a battery.
Allowing people to transfer magic/money between clips on their own is fine. The amount of magic in the economy remains the same. Individuals are prevented from adding magic to the economy, the only way they can add magic to their clip is from another clip.
Money can be added to the economy the same way we do now, via a central bank. The central bank authorities are allowed to make and charge clips creating new money. They then loan them to banks to add that money to the economy. They can also borrow money to remove money from the economy. By controlling the interest rate at which they loan and borrow money they can indirectly speed up or slow down the economy.
This is fine for fiat money, or even representative money, but yours is commodity money. That means people are allowed to remove money from the economy by using the magic contained within it. While some money is always lost in any system, this happens at a fairly predictable rate. Your system adds a wildcard to the monetary policy. Certain economic conditions will cause more people to turn their money into magic causing deflation. How this works out depends on how magic works in your world and under what conditions people are likely to start using money as magic instead of as money.
Then there's the problem of international currency exchange. With fiat money this is controlled by market forces relating to the strength of national economies, but yours is commodity money. That complicates things. There is the face value of the money, and then there is the commodity value of what it is made of (ie. the magic).
If the face value is higher than the commodity value, you're ok. Currency will be traded on the exchange according to market forces. The problem comes when the face value is less than the commodity value. This can happen because your economy is undergoing inflation, or because the value of the commodity has increased. Now you have a problem. Speculators will enter the market, buy up the undervalued currency, "melt it down", and sell the commodity.
On the one hand, your government just subsidized someone else's Get Rich Quick scheme and lost a lot of money at a time when their economy probably isn't doing so well. On the other hand, a bunch of surplus money was just removed. Reducing the money supply should hopefully increase its face value, while also increasing the magic supply to lower the price of magic.
Since it's international there's opportunities for arbitrage: making money off price differences in different markets. If magic is cheap in one place, but expensive in another, people might buy up currency at the cheap location, melt it down, and sell the magic on the other market for a good price. Eventually the prices will equalize, but meanwhile the money supply is being messed with.
Finally, authorized commodity money like coins or your system acts as a price cap for the commodity in question: the central bank creating the coinage is effectively selling magic at the face value of the money. The value of magic (or gold, or silver, or whatever) will never go above the face value of the money. If it does, people will buy money instead and melt it down. This can have serious consequences on any industry which relies on or creates magic. By keeping the price below where it would be by market forces, it can further restrict the magic supply in a time when the suppliers should be increasing production causing shortages.
Point is, commodity money can complicate the international currency markets. You might be better off going with fiat currency and using magic to implement the transfers and prevent counterfeiting.
Whew. Well, that's currency economics 101. Hope this helps!