USPS (the postal service) is the only way to ship without it costing a fortune, and even they are not cheap these days. Unfortunately, a 24" bass is going to be bigger than you can fit into a box that they will accept.
I just shipped a kit to Austria using IPS (22,16,12,13) and it ended up being more expensive than the original quote they gave me.
IPS gave me a quote for an air freight service that seemed cheaper than UPS or FedEx, but there were pickup charges that in the end cost the same as FedEx.
IPS does in fact give you options in shipping. FedEx is one of them, and the price to ship FedEx by using IPS may be cheaper than going to FedEx directly, but it definitely took longer to ship with IPS.
My advice is to look at IPS pricing for shipping, but stick with their FedEx options, and ask questions about any extra pickup fees.
Shipping has become more expensive in the last few years, and shipping a 4-5 piece drum set with a 24" bass drum to Europe is going to cost at least $600-$800.