I’d like to deposit my valuables and my passport into the hotel safe.
Your trip ticket is the ticket that lets you go on ALL of your trips. It's not your airplane ticket, it's not your boat ticket, it's the trip ticket. It's your passport, which allows you to take trips.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.