The fact that you get an image produced in the EPS file is because there is a transparency in the file, when the eps is produced the transparent object and any objects underneath it get flattened (rendered to an image) as they cannot be translated to vector objects, hence the bitmap and vector combination in the files.
If you go to Options > PostScript Setup > you can uncheck the option for “Intelligent Resolution reduction”, you then have 5 resolution options on the sliding scale that you can choose. I would suggest just switch off the resolution reduction and try that first, and then try adjusting the resolution setting higher if the quality is still not good enough.
The image resolution looks to be 300x300 dpi at the highest setting, but if the print is very large the image sizes can become very cumbersome at this DPI.