Actually, sRGB is a color working space, not a printer profile. The terms overlap a little bit but they're not exactly the same thing. No printer is ever going to print correctly if you use sRGB as a destination print space. If you want to print correctly from Photoshop, the first thing you need to have is a good ICC profile of your printer, printing in the resolution you're using and on the media on which you're printing.
Then, your image may be in any of several 'working spaces', such as sRGB, or Adobe 1998 RGB, or ProPhoto; and your goal is to get a conversion from your working color space to your printer color space (ICC profile) while keeping as faithful as possible to the colors as they exist in your original color space.
You do this by telling the printer to shut up and do as it's told--hopefully the instructions are in the driver somewhere--and by having Photoshop manage color, and selecting your printer profile as the destination color space (ICC profile).
Of course understand that unfortunately a valid ICC profile isn't necessarily a good ICC profile. Making printer profiles is an art, and there are a lot of downloadable profiles out there--even from some pretty well-thought-of media, ink, and printer companies--that just aren't very good.
Still, the path outlined above is the only way to do it correctly, and how much time and effort and money you put into getting a professional-grade color workflow is entirely up to you.