There are few questions to explore. Although the money is muktzeh, does it make the suit jacket muktzeh? Even if the jacket is not muktzeh, may one continue to carry around the money?
The matter has to do with the halachot of bassis l’davar ha’asur, an object that is intrinsically not muktzeh but is supporting a muktzeh object. The basic halacha is that the bassis is muktzeh and that if this situation existed when Shabbat began, it cannot be moved even after the muktzeh has been removed from it.[1] At first glance, your case satisfies this condition. However, there are many exceptions to the rule, and it is likely that at least one of them applied to your case and could have partially solved your problem.
Suppose that two fundamentally separate objects are firmly attached, and the more important part of the joint object is neither muktzeh itself nor does it have muktzeh directly on it. If the less important part is a bassis l’davar ha’asur, the joint object is not muktzeh.[2] A suit with pockets sewed onto it is a good example, as the suit is more important than the pocket attached to it. Therefore, if the pocket has money in it, the suit is not considered a bassis for the money or for the pocket, and the suit can be moved in spite of the fact that the pocket moves along with it. However, the pocket itself can still be a bassis l’davar ha’asur. Thus, one should not stick his hand into the pocket,[3] even when the money was already removed after Shabbat had started and even in order to remove the money.[4]
There is a different type of pocket that is made by having part of the main fabric of the garment serve as part of the pocket. In such a case, if there is muktzeh in the pocket, the whole garment can be a bassis l’davar ha’asur.[5] Shirt pockets are a classic example, but there are jackets that have some pockets that fit this description.
There are other reasons that a garment may not be a bassis. A basic requirement of that status is that the muktzeh was placed on the potential bassis with the intention that it stay there on Shabbat.[6] If a garment is regularly worn on Shabbat, the assumption (without a need for cognitive thought) is that one did not intend for the muktzeh to remain there until Shabbat.[7] In that case, even the pocket itself would not be muktzeh. In fact, even if the suit was meant to be used primarily during the week, it still would be unlikely for the pocket to be a bassis. Most people do not purposely leave $20 bills in their pockets, irrespective of the laws of muktzeh. Assuming you meant to take the money out of the pocket either a few minutes after you put it there, or at most at the end of the day, there is no issue of bassis l’davar ha’asur whatsoever.
There is a machloket about whether one who is wearing a non-bassis garment with muktzeh in it should remove the muktzeh as soon as possible.[8] We usually try to remove the object at the first opportunity.[9] However, there are several legitimate excuses to delay doing so.[10] Included in this category are: when a loss will likely occur to the muktzeh object (e.g., someone may take the money); it is difficult to do so without removing the clothing;[11] when it will be embarrassing for the muktzeh to fall out or it will be an eyesore. Therefore, if there was no issue of a bassis garment in your situation (as discussed above) and if, for example, it would have been difficult to remove the money in such a way that you could retrieve it after Shabbat, you could have waited until you got home or to a private place before emptying out the $20 bill.