You are probably using daylight balanced film. It only has 1 white balance: 5600K. If you shoot it in overcast, shady, or other than direct sun or lights that simulate sun light, it will appear cool. You can get color corrective filters for this. Google "color temperature".
The age of the film can affect colors. Check the expiration date. Keep film cool as possible to slow aging.
The lab you have do you processing and printing may make a huge difference. The developing is all pretty much standard. As long as they are maintaining the machines and chems any place should be able to develop okay, but printing good color is much more about the opinion and experience of the print machine operator. You might try a better lab, and see if they give you better results.
High ISO film often has lousy color, but you shouldn't have any problems with ISO 100 or 200.
Under exposing will tend to reduce saturation and contrast for print film. You might try halving the recommended ISO (shoot 100 at 50, 200 at 100). This is only for print film not slides.
Exposure can be adjusted to affect contrast, but it's most effective when you can also customize the developing, and that's not a common or cheap option.
Try a polarizing filter. It does amazing things for color with both film and digital.