QE really doesnt make that much difference, it only affects the bond market directly a bit. VC is getting more money as the returns have been good (finally, historically they werent), while say hedge funds have had bad returns. The amount of money in private markets depends highly on risk preferences.
This is not quite accurate. Sure, directly it only affects the bond market. But the bond market is not isolated from the rest of the markets. After you push loads of money into it, it lowers the returns on relatively low-risk bonds. We now are seeing government bonds with near-zero interest rates (ZIRP). The low returns on bonds pushes capital that otherwise would have gone into those bonds into risker and risker assets, a direct consequence of QE. This has people chasing higher returns in stocks, and yes, VC as well.