It seems that your squadron has made stuff up do to perceived lack of guidance in, or inadequacies with, the drill manual. I would encourage them to rethink; not least because what you describe is awkward.
A salute by a banner bearer is nothing more than “letting fly” at the carry, be that static or when marching past in quick time. No dipping involved. A salute on the march in slow time sees the banner dipped to the horizontal.
On the occasion of a “Royal Salute” on a static parade it is a bit fancier, with the banner let fly, then brought horizontal out to the right and then brought to the front and lowered to the ground (see AP818 Pr1, Ch9, 11).
I’m not really sure what you are doign or the circumstances in which you are doing it, but if letting fly the banner isn’t appropriate at the time then my advice would be just re remain at attention at the Carry or at the Order, depending on the stage of the parade, the length of parade, the strength of the bearer and what the Parade WO decides
There is no “present banner” movement - what does this entail in your experience?
There is a “port banner” as if to hand it over, but the banner equivalent of the arms drill “present arms” is the salute as detailed above.
NOTE: AP818 is written with RAF Colours (and standard) in mind, not lowly ATC unit banners - only the ATC banner is afforded equivalent honours and many of the salutes detailed are TO the colour, not from the bearer. With the exception of The Banner of the Air Training Corps, ATC banners are not afforded complements.