Is there a technical term for this simple method of smoothing out a signal?
What you've implemented is a single-pole lowpass filter, sometimes called a leaky integrator. Your signal has the difference equation:

$$
y[n] = 0.8 y[n-1] + 0.2 x[n]
$$

where $x[n]$ is the input (the unsmoothed bin value) and $y[n]$ is the smoothed bin value. This is a common way of implementing a simple, low-complexity lowpass filter. I've written about them several times before in previous answers; see [1] [2] [3].