According to BA's website there may be some exceptions made for sporting goods which may mean they will allow you to exceed the 190cm rule. May be worth asking.
If you want to be creative find a box that matches the 190cm x 75cm limit and put the rod case in diagonally. You should get an extra 4 or 5 inches that way. Not sure how big a bicycle box is but I've used those before as you can get them from an Evans store for free.
K