Actually, it's a Chinese idiom - and I've had lots to say about such idioms in the past. Literally it means "When the boat gets to the bridge-head, it will naturally go straight", or in other words, "Everything will be alright."
I made a note to copy this into my flashcards, and when I got home I typed "船到" into my dictionary, only to discover that there are actually a few idioms that begin when the boat arrives.
Without much explanation, for your interest, amusement & education, here they are:
船到江心，补漏迟
chuán dào jiāng xīn, bǔ lòu chí
Once the ship has reached the middle of the river, it's too late to plug the leak
(English equivalent: No point in closing the stable door after the horse has bolted)
船到码头，车到站
chuán dào mǎtóu, chē dào zhàn
The ship has docked, the carriage has reached the station
(The job is over, it's time to relax)
船到桥门，自会直
chuán dào qiáomén, zì huì zhí
When the ship arrives at the bridge we can deal with the problem
(No point in worrying until it actually happens)
And actually, there are a few such idioms which talk about cars arriving too:
车到山前必有路
chē dào shān qián bìyǒu lù
When we get to the mountain, there'll be a way through
(The same meaning as the opening idiom about boats)
车到山前自有路
(A slight variation of the above)
车到山前必有路,船到桥头自然直 车到山前必有路，船到桥头自然直
chē dào shān qián bìyǒu lù, chuán dào qiáotóu zìrán zhí
When we get to the mountain, there'll be a way through and when the boat gets to the pier-head, it will go straight with the current
(This is a mega version combining both ships & cars)
Make sure you quickly copy at least one of these into your flashcards NOW, before you realise that your ship has sailed :-)