The best option is to invest in an ATA case.
If you can't afford to do that at this time-
You won't be able to take the bass on-board in a HSC.
It's very unlikely, although there's a slight possibility. that you can take the bass onboard in a gig-bag, and they'll store it for you. Real unlikely though, don't count on that at all.
I flew quite often with my bass, and used this method with no problems whatsoever-
Have a UPS store make a heavy-duty box for your HSC.
Cost me $25'; I still have it.
At the check-in counter, explain that it's a valued musical instrument, and ask for Special Handling.
They'll mark the box with "Fragile" and "Special Handling" decals, and in my case, I walked it over and talked to a Baggage Manager.
Despite some people's horror stories about lost and damaged luggage, I got nothing but consideration and understanding from the Airline personnel. They took pride in what they did, and several times, they told me about their own musical projects! Kind of contrary to those who seem to enjoy dissing the Baggage Handlers as Gorillas... but, hey, if that floats your boat...
I took over 15 flights with my bass shipped in this manner, and every time, it came to me intact, in the "oversize" section of baggage claim.
Believe it or not, packages checked in and marked for Special Handling get that. There's accountability for baggage and cargo, and the crews like to keep a good record of having packages marked as such undamaged.
Communication and good packaging go a long way!
Good luck, have a good gig- Italy is awesome! Unbelievable wine (and women). Bon Voyage.