Mapping from Object => with a Bump Map?

[tyFlow]

When you apply your mapping overrides, just assign them to a map channel that doesn't contain your mesh UVWs. So for example, channel 2. Then make sure to apply the override map (in this case, the Checker map) to the same map channel. Assuming the bump UVWs are in channel 1, apply a bump map to that channel and it should all work together.