I've never ridden the SP2 with passengers, but in my younger years used to do a lot of riding on my VFR750 - 2 up. Sometimes for days at a time, when touring in Europe with a girlfriend, or doing fast rides through the English countryside.
I think 3 things are important. Firstly that the bike's well suited to carrying passengers.
My previous 954 'blade was rubbish for this. Absolutely nothing to hold onto for support and it would perch the passenger much higher than the rider. You need a proper sturdy handle at the rear at least.
The 2nd factor is confidence. The passenger must know how to position herself and use the tank (& rear handle) to give support from braking, and also when accelerating.
She will have to lean into a corner with you and follow your movements instantly.
She has to enjoy riding on the back (& this goes hand-in-hand with comfort).
You also have to be confident in your abilities and the bike's.
The third thing that's important is clothing of course. SBoth of you need to have the right protective gear.
The RC51 isn't the right bike, but if you take it sensibly and she enjoys it, you'll be fine for a relatively short distance. It's not a bike for a 2-up touring trip though! If your CBR600 is an F rather than an R model it might be better than the RC51.
If she really enjoys it, think about buying a good bike for riding 2 up with...
But keep the RC51 for yourself
Euro RC51 SP2: HRC WSB Ti Hi-Level, T1 Airbox & Snorkel, PCIII, Dymag CA5 Carbon Wheels, Ti64 Spindles (F, R & Swing Arm), Mori Link, Maxton GP7 Shock & Ohlins 832 Forks, Brembo GP Calipers & SBK narrow track (F), Braketech Disc (R), Brembo billet Underslung x 2 Brembo RCS, Tyga Triple, 7075 Stem, Probolt Titanium all over, Babyface rearsets, MR Complete Carbon Lineup, Custom Undertail & CBR 1000 LED, Watsen LED Indicators, Harris Brace, Giles clip-ons, Corbin seat, etc. 2013 BOTY.