You might glue and screw plywood for peace of mind.

I'm not sure how that would make a difference as far as the strength of the joists though not being strong enough to support the load

Believe me,it make's a huge difference. Seven and a quarter inch wide 1/2" plywood is stronger than a 2x8 fir board. 3/4tr inch plywood is more than twice as strong and plywood resist's flex better. I suggested ply wood not only because it add's more strength,it's cheaper and weigh's less making it far easier to hold in place while installing. I suggested glue because it has more holding power than nails or screws. I suggested screws because they beat clamping while glue dries. I suggested screws instaed of nails because they are eaiser than nails in tight quarters.

For something this critical I would recommend calling in a professional engineer. Advice here is good but....

Thanks for the responses. Lets say I do take care of the deflection with a layer of 3/4 plywood. Is there a danger based on the joist span that I am exceeding my dead load due to the tile, and shower glass, vanity, etc?

" Is there a danger based on the joist span that I am exceeding my dead load due to the tile, and shower glass, vanity, etc?"

I certainly hope not but as Tim45 suggested,call in an engineer if you are still worried. This is a diy place with guys that have btdt and a few pros retired from the trades. Engineers are a funny bunch,they will not tell you a 2x8 will support a butterfly if he land's on it unless they come out and study the situation. Hence you aren't likly to find one here. Most of us fly by the seat of our pants based on experience,rely on common sense and just overbuild it since it only cost's a few dollars in extra material but no labor. An addition I put on my house 12 years ago has an 11" beam glued up on site from 5 layers of 3/4tr" plywood . 19 feet free span supporting fourteen 16'ceiling joists, 9 17' gable roof rafter tails plus one end of a 16' rat run supporting center of ten 2 piece 16' ceiling joists. When I did the beam I looked back collectivly on several engineered beams I had used and seen in the past. If my life depended on it,I couldn't tell you what the engineering specs on that beam are but after 12 years it's still string straight.

:) thanks for that answer klem1

Great advice

The code required design loading should be more than adequate for this bathroom since it apparently doesn't have a whirlpool spa or even a standard tub and it is unlikely to be filled with people. Using the IRC joist span tables for an upper floor (30 psf LL & 10 psf DL) the max allowable span for SPF lumber would be 13-6 but for your D. Fir #1 framing the max span is 14-1.

For your joists the deflection under full design load should be closer to L/410. That means the joists should be stiff enough if they are properly supported and have no notches or other defects and the decoupling feature of DITRA should prevent tile cracking assuming adequate subfloor and underlayment.

As for comfort, the span is not long enough to cause much floor shake but if you want to be safe, try a heel-drop test (stand on your tip toes and drop your weight onto hour heels). If the floor doesn't shake, it doesn't need reinforcement.