Cycle-exact is not directly related to blitting. It slows down the entire emulation because it syncronnises the CPU and the custom chips to the exact cycle counts like on a real Amiga.
If you write into the screen's bitmap, the blitter is not used. But in case of cycle-exact the update is captured and promoted to the display immediately. This massively slows down the code. You should not use cycle-exact emulation and especially you should not write code which needs cycle-exact emulation. This code won't be compatible to different Amiga models with different custom chip versions.
As suggested above you should render into an off-screen bitmap and then blit the entire picture into your Window or screen.
Bye,
Thomas