Hi there,
I searched in Japanese and found out that there are 2 ways to get Izu Craile.
1. Purchase "Japan Rail Pass"
It includes the fare for Izu Craile. If you trip around within the covered area of this pass, it might be a good idea.
2. Visit the tour center, travel agency
Izu Craile offers some plans so that you (even me) can't find the fixed price.
ex) with coffee, with dinner etc
I found Japanese website which shows the plans and the prices, but it seems no English website.
If it will be a little help for you, please see below.
http://travel.eki-net.biz/jrnetsbyu/servlet/CommodityListServlet?keywords=%E4%BC%8A%E8%B1%86%E3%82%AF%E3%83%AC%E3%82%A4%E3%83%AB%E3%80%80%E3%83%A9%E3%83%B3%E3%83%81%E3%82%BB%E3%83%83%E3%83%88&m1=0&m2=0&usecf=on&cf2=%E6%97%A5%E5%B8%B0%E3%82%8A&_ga=1.233209566.1518444871.1489928367
( this includes lunch, 1 Izu Craile ride onward trip, round trip between Tokyo and Shimoda station)
http://travel.eki-net.biz/jrnetsbyu/servlet/CommodityListServlet?keywords=%E4%BC%8A%E8%B1%86%E3%82%AF%E3%83%AC%E3%82%A4%E3%83%AB%E3%80%80%E3%82%AB%E3%83%95%E3%82%A7%E3%82%BB%E3%83%83%E3%83%88&usecf=on&cf2=%E6%97%A5%E5%B8%B0%E3%82%8A&_ga=1.229972700.1518444871.1489928367
( this includes coffee, 1 Izu Craile backward trip, round trip between Tokyo and Shimoda)
Hope this can be your help..