I would presume that if someone like Bilbo came back to The Shire with a lot of gold that was not in the form of Shire currency then he would have had to exchange it in some way. Now, if The Shire had currency, then it would also need the bullion to make it from, which presumably would not be all that easy to come by! Therefore, Bilbo could well have passed his bullion on to the 'treasury' or 'mint' in exchange for coinage.
I am not sure if there were banks though, so maybe Bilbo
dd have to hide his money in the cellars of Bag End?
I interpret the class structure of The Shire differently. It is clear that the Bagginses are solid Middle Class. Tolkien made it clear that they were quite ordinary, with conservative views, just well off. Bilbo is a fantastically well observed, and gently satirical representation of an English middle class male: likes to read, suspicious of strangers, keen on routines such as teatime, likes small pleasures such as a nice cake. I'm not sure whether his type is dying out nowadays. Putting those things together these days might be seen as creating a less sympathetic character.
Merry and Pippin are clearly of the 'old' aristocratic class, together with the teeming family and the sprawling family home (the 'country estate'). The Sackville Bagginses are a joke of Tolkien's either on the part of Middle Class intellectuals (like the Bloomsbury set, which included Vita Sackville West and Virginia Woolf), or on those who were Middle class and sought to make themselves more aristocratic e.g. by acquiring a double-barrelled name. I've heard Tolkien was quite sporty in his youth and slightly suspicious of more 'aesthetic' types.
Frodo may well have earned much income from quiet investments, maybe a little rent here and there on property or land. Was he left with any money of his own after his parents died?
The Shire is not feudal, it is more advanced. It is more like turn of the century (19th/20th, not 20th/21st!) Britain, but without a Government and all the machinery of State.