I just want to make sure I'm understanding the bow limit rules for rohan.

This would be an incorrect warband due to the fact that riders of Rohan don't count towards the bow limit.

Eowyn
3 Rohan Royal Guard
3 Rohan Outriders
2 Riders of Rohan

This is like having 6 models in the warband counting toward the limit and not the full 8 correct?

Thanks in advance.

Yes, what you said is correct. The Riders of Rohan are ignored when it comes to calculating your bow limit.