Out of interest, if you were flying a light aircraft, would you tell passengers what checks you were doing and say them aloud or just do them silently? I may have my first passengers next week!
No apology needed at all, in fact congratulations on finishing your training-they say you always remember your first solo but I cannot rember mine but I can vividly remember carrying my first passenger and it did not go very well. While I was in the local area the tower radio failed and the passenger became very concerned when she could hear that I was continually transmitting and not receiving any reply-she started to ask me continual questions which made it more difficult for me to decide what to do!
Before I get to your question I will tell you about two other pax I had on first light aircraft flights(theirs).
I took off with a guy who had his mother in the rear seat just after lift off she started screaming and I do meaning screaming- She was having some sort of fit and frightened to death, she continued screaming all the way around my short circuit until I touched down making it very difficult for me to fly the aircraft and talk to ATC.
Years later I was doing pleasure flying at a flying display and just after lift off a woman in the seat behind started screamimng in the same way. Of course the experienced Captain Pull What now knew exactly how to deal with the situation. I turned to her and said, " Dont worry, stay calm, I will make an immeadiate return to the airfield -she replied, (and I quote exactly) " Why, this is absolutely Fxxxing marvellous"!
No I would not personally shout out checks aloud to pax but if you feel happier doing this thats what you must do. You need to give the pax confidence, the use of a written check list helps with this, even if its only a token gesture.
If your passenger has never been in a light aircraft before be gentle but confident!
Oh and don't do what I did one day:
I was boarding the aircraft with the pax down the jetway after completing the walk around, a passenger said to me, "is it good flying conditions today captain i am a nervous flyer"? I replied, " its fantastic and dont worry I am feeling extremely lucky today"!