Many violinists have some powdered rosin somewhere which is great for "starting off" a new bow with rosin - like you've observed, it's quite a tedious process otherwise. I'd stress that it does bed in eventually, and will work, but you need to keep at it for a fair while (I've done it this way on many occasions.) As mentioned above, you can also use sandpaper to "shave off" some powdered rosin from the block, essentially mimicking the behaviour of the above.
Powdered rosin does get a bit messy though - for a long time I actually used cello rosin with my violin - the difference is it's a bit softer, and again this can help it grip much better to fresh hair. So if you plan to try out many new bows, that may be a good investment for all it costs (not much.) Double bass rosin would be softer still, though in my experience this is so soft that it can get way too sticky in warm weather, which tends to make it go everywhere.