There are several answers but I suppose none of them deal with the question properly. I will try to explain from my opinion whats going on and what you are reading in newspapers might be sensationalized but it is definitely not far-fetched propaganda either.
Bankruptcy is declared when a person or entity cannot pay its debts and sometimes that entity can be a country. To be fair, Saudi Arabia is not going bankrupt because it currently doesn't have any debts but its blowing a big hole in its bank and running on steroids towards financial ruin.
First of all, no country can be bankrupt at the present time because no country's debt has ever been issued under laws that allow for bankruptcy to avoid repaying debt.
What you really mean to ask is if Saudi Arabia can ever default on its loans? However, even in that case the answer is that it is very, very unlikely. All Saudi Arabia has to due to avoid default, is to avoid borrowing very much and to reduce government spending, something Saudi Arabia has been quite good at compared to most other countries. Enjoying one of the lowest costs of oil drilling in the world, plus a very small population of its own to provide government services to means that Saudi Arabia can manage quite well on a relatively small budget if it has too, which also means that it can probably borrow as much as it wants from investors so won't really ever have to worry about any drastic reduction in public spending like so many other countries have to(i will say they are lucky in this regard).
Saudi Arabia can produce oil at a very low cost. US shale gas producers on the other hand are high cost producers.
The new energy supplies from the shale gas producers make it difficult for OPEC to raise oil prices. But OPEC led by Saudi Arabia, or Saudi Arabia acting alone, can cause the prices to fall. This is what has happened in recent months. The move has had the effect of shutting down most shale gas producers. More importantly, it has also put revenue squeeze on some higher cost oil producers such as Russia and Iran.
Naturally, in this scenario, Saudi Arabia faced declining revenues from its oil exports. The result was budget deficits, which the Saudi government financed out of its massive currency reserves. This cushion is available for now and for some time into the future. Now Contrast this situation with that of Iran, which finds it more difficult to finance its budgetary outlays because in addition to declining oil export revenues, it has been facing sanctions over its nuclear program(even though we are now lifting sanctions against Iran).
The Russia's situation is not much different. The government finances and the Russian economy are under great pressure from falling oil revenues and western santions imposed after the Ukrainian crisis.
One way of looking at the unfolding scenario is that Saudi Arabia has turned on the oil taps to win back energy market share from the shale gas producers, while at the same time imposing economic punishment on its regional rival Iran. The fact that the nuclear deal with Iran was reached in the backdrop of falling oil revenues lends some support to this view.
Saudi actions in the oil market also seem to be in line with the US foreign policy vis a vis Russia because by inflicting more pain on the latter country, the lower oil prices reinforce the impact of western sanctions.
So the point is that the Saudi oil market stance may not be seen in the context of the oil market alone. It has both economic and geopolitical repercussions.
As the global economy recovers, and the geopolitical situation changes, Saudi Arabia could reverse its oil policy. In all likelihood this would happen much before the point where the continued budgetary deficits start playing havoc with the Saudi government's finances.
The nuclear deal with Iran might pave the way for the release of the frozen Iranian assets. Then the economic pressure on Iran would lessen considerably. The geopolitical impact of the Saudi actions would also diminish. Would that be the time for Saudi Arabia to reconsider its oil policy?
