The wait can differ. It all depends on your comfortability level. My wife didn't understand why I just didn't take her for a ride. She now has her own bike and understands. The extra weight will make a difference. You may not notice at first, but the more you get used to your bike, you'll feel a difference in the response. When I first took my wife for a ride, it was like, wow... a little more heavy. That was about 6 months ago. Recently when I took her for a ride (no resetting of preload/rear shock) I felt the front end wanting to lift up and not grabbing as much as when I was on it by myself. It was only for a short hop, but I was extra careful with her on it. Just get comfortable on the bike first before you start taking on passengers. Couple of things though if you're going to ride 2 up.
1) Get her proper gear. Helmet, gloves, riding jacket, ankle-high boots, etc.
2) Sit in the driveway a while and get a feel for the extra weight. You may want to adjust the preload and rear shock for long distance riding
3) Practice by going around the block or in a parking lot until you feel comfortable.
4) Don't take off too fast or she'll fall off
5) You'll probably need to use a little more throttle with her on. Depending on what type of bike you have.
1) Hold on tight (not enough to suffocate you though)
2) Which ever way you look and lean, she should do the same exact thing. Don't try to lean the other way (counterbalance) even though she thinks the bike will fall over. It may cause the back wheel to come around and you'll lose control. Trust the bike.
In taking corners, it's best that she leans into your back for a good center of gravity. There's a big difference in cornering if she's leaning into you than if she's sitting straight up.
3) Don't shake too much or adjust her seating position from one side to another. It's possible that she can adjust her seating if she uses BOTH feet on the pegs to keep everything centered when you're riding, but it's best when you're stopped. Kinda like standing up a little.
4) This is important! When coming to a stop, have her brace herself (with her arms and legs) against you or to hold on to the luggage racks so she doesn't slide into you when you're coming to a stop. That HURTS! Unless you're wearing a cup.
5) She can also help by using hand signals to people behind so they know which way you're turning.
Hope this helps. If I think of anymore, I'll post another.