How was Napoleon's military funded just a decade after the French Revolution ostensibly because of bankruptcy/mismanagement of funds?

From 1799 (when Napoleon became First Consul of France) to 1805, the French treasury was most dependent on taxes from France and its empire. After 1805, conquered territories in Europe such as Spain, Italy, Austria and Prussia made increasingly large contributions to French military costs through (1) taxes, (2) peace settlements, (3) the seizure of property etc., (4) the supplying soldiers at their own expense, and (5) paying for the cost of French soldiers stationed in their territories. In 1813, after the disastrous retreat from Moscow, some money was also obtained by selling communal land.

Throughout the Napoleonic era, borrowing was - out of necessity as much as design - kept to a minimum, though it did contribute to the state's financial resources. I can find no evidence that the Catholic Church made any significant contributions, though money did come from Italy as a result of conquest. Napoleon also shied away from simply printing more paper money as the Directorate had done. Instead, the focus was increasing tax revenue:

Napoleon's coup of November 1799 began sweeping changes in government finances that built on the tough measures taken by the Directory. The system of taxation was reorganized, new taxes were imposed, payment on the debt in specie was resumed and institutions - the Banque de France and a sinking fund - were established...

Source: M. Bordo & E. White, 'British and French finance during the Napoleonic war'. In The Journal of Economic History Vol. 51, No. 2 (Jun., 1991)

Also, "proper incentives for effective tax collection" were introduced. However,

Although collection of direct taxes improved with these measures..., the government did not rely on direct taxes to cover its expenditures....during the Empire, indirect taxes were gradually re-introduced....New taxes, similar to those of the ancien regime were imposed on tobacco, alcohol, salt and the prices of government monopolies, such as the post were increased.

Source: Bordo & White

Consequently, taxation became much higher than during the revolution and public debt grew very little up until 1814. Although the data is incomplete, Bordo and White cite figures which show that tax receipts as a percentage of Commodity output were around 5% for the years 1791 to 1796; between 1806 and 1814, this number ranged from 14% to 20%. Some borrowing occurred through long-term bonds and from the banque de France but, even when this peaked in 1805, the latter was less than 10% of expenditure. In part, the limited borrowing was due to France's lack of credibility in the markets.

From 1805, conquered territories began to make increasing contributions to French finances. For example, Austrian taxation rose from 75 million francs in 1805 to 164 million in 1809, while Prussia contributed between 470 and 514 million francs in the years 1806 to 1812. Further,

The theory expounded by Napoleon was that his campaigns abroad should be self-financing. The three methods used to achieve this goal were: the seizure of money and property (so-called ‘ordinary contributions’ or saisies ordinaires); the financial gain derived from peace treaties; and the amounts saved via the policy of using allied troops or by having French soldiers maintained by the allied states in which they were stationed.

Source: Pierre Branda, 'Did the war pay for the war? An assessment of napoleon's attempts to make his campaigns self-financing'. In Napoleonica. La Revue 2008/3 (N° 3).

In reality, the wars were not self-financing despite Napoleon's insistence on a comprehensive accounting system, but the contributions from the conquered territories were nonetheless significant; Branda has calculated that these contributions amounted to around 42% of the cost of the wars.

Finally, some money (but much less than projected) was raised by selling communal lands. This desperate measure was brought about by the failure of the Russia campaign, the consequences of which were dire:

The Russian campaign alone had a price tag of 700 million francs. With this tremendous strain on the nation’s finances it is not surprising that the deficit increased each year. In 1811 the shortfall was a modest 6.5 million francs; by 1813 France had a 149 million franc deficit.

Thus, a law was enacted in March 1813:

...the state would seize all communally held lands that were leased to individuals; these lands would then be sold at auction with a guide price of 20 times their annual revenue. Villages would receive a fixed sum of five per cent of the ceded lands’ value from the government in return for their lost assets.

However, of the anticipated 370 million franc 'windfall', only something in the region of 60 to 90 million was realised.