Understanding the Bohr Model does not really help you for this concept. You rather need to know about different kinds of covalent bonds, some organic chemistry and physics.

Molecules with C-C single bonds have their electrons fixed in the molecule and these molecules absorb in the ultraviolet and are colorless. Molecules with double bonds often can spread the electrons over the molecule and they absorb in the visible light and have a color.

Now, the plant pigment molecule cyanidin is a quite complicated organic molecule. All you have to understand, however, is which form has the electrons in a more fixed stage and in which form can the electrons move more freely.

Normally you have to look at resonance structures. For cyaniding, the acid form is the one where the electrons are fixed (high energy form) and the basic form is the one where the electrons can move (low energy form).

You also need to know the visible part of the electromagnetic spectrum. Going from low energy to high energy the colors appear red, orange, green, blue, violet and then ultra violet. So a red shift means a shift to lower energy and a blue shift means a shift to higher energy. If a molecule goes from a high energy form (fixed electrons) to a lower energy form (mobile electrons) the molecule does a red shift. When the molecule goes from low energy form (mobile electrons) to high energy form (fixed electrons) it does a blue shift. Now lets look at the colors:

I already said the acidic form of cyanidin is the high energy form with the electrons more fixed. The molecule is red, because it absorbs violet, blue, green light. Now when the molecule is in a basic solution it undergoes a red shift in absorption. The plant now absorbs in the yellow, orange, red area and this makes the molecule appear blue.