Q:

In 4/4 time can I insert a half sized bar in the middle of the piece?

I am writing a piece that has a chord structure A, B, A, B,etc. with a melody that is not repeated.
When ending the B part the music wants to hang for an extra two beats before returning to the A part. It then means that my second A part starts in the middle of the bar unlike the first time around. 
Can one insert half a bar to keep the uniformity or is there a way of showing a slowing down of the last two quarter notes by half so that in effect they become half notes? Or should I not be worrying about the fact that the part starts halfway through the bar? 
As you can no doubt gather I am a novice at music notation.

A:

I'm not totally sure I understand what you are trying to achieve, but this might help:
There is no reason why you cannot change the time signature for just one bar, and then immediately change it back to what it was. For example, after a number of bars of 4/4 music, you can insert one bar of music with a new time signature of 2/4, and after that "half-sized" bar, go back to the previous time signature of 4/4.
Would that solve your problem?

A:

This has been said many times already on this site, but here goes...
The answer to all “can I do X”-questions in music is: yes, you can do anything!
Really, these questions have just two subquestions that should be considered:

“Do I want it”? Everything you put in a composition will have a certain effect on the end result. If you decide to put an F♯ in the melody of a piece in F over a D minor chord, nobody can stop you. It just will sound, ahem... Or to take a more relevant example, it's perfectly possible to use parallel fifths, and it won't sound wrong (except perhaps to some overzealous music educators), but it also won't give you quite the full intertwined-harmony sensation that classical composers achieve with their 4-voice counterpoint (which generally avoids parallel octaves and fifths, though even those composers make exceptions when it's musically useful).In your example, this questions reads “will it sound disruptive if I insert a single ²⁄₄ bar in the midst of my ⁴⁄₄ piece”? To which the answer is, possibly, but since ²⁄₄ is still pretty even, it will probably be barely noticable. In fact, if that extra half-metre fits logically in the melody, then it will likely sound less disruptive than the pause that a full ⁴⁄₄ bar would incur†. So by all means don't shy away from that possibility, just be sure that it actually feels right.Whether something feels right is best determined by actually playing it, even if just in a much simplified manner.
“Is it practical”? Some things might theoretically work out great, but it's unrealistic to expect the musicians to be able to accurately render them out. Obviously this includes technically very difficult lines (it's always good to know yourself at least roughly how everything would actually be played, on each instrument), but also parts that are rhythmically or otherwise too hard to get together. And many musicians aren't capable of playing complex metres. But again – ²⁄₄ really isn't that far-out, almost nobody who's musical at all should have trouble with that. As already said, it's not uncommon either.

Is summary: yes, I reckon you should insert a single ²⁄₄ bar in that piece.

†Then again, it can be good to have a bit of space. A rest in the main voice may be an opportunity to give e.g. the cello a bit of a melodic hook, or just to de-clutter everything.

A:

Instead of changing time signatures, you might consider instead using a pause (fermata) on the last 2 beats worth of the last bar of section B.
I assume you are considering writing something like this at the end of your section B:

Instead you could consider doing this:

This may not be precisely what you want though.  According to the wikipedia entry:

Exactly how much longer it is held is up to the discretion of the performer or conductor, but twice as long is common.

