Expanded standard deviation in logarithmic scale
It's a mathematical problem.

Let's look at a simple example and say you have a sample with mean \$\bar{x}=100\$ and \$\sigma=10\$. 

If you convert each value separately, you get

\$\log_{10}(\bar{x})=\log_{10}100=2\$
 \$\log_{10}(\sigma)=\log_{10}10=1\$

So, is the result really \$2\pm 1\$ ???

Standard deviation means that 68% of all values are within \$[\bar{x}-\sigma;\bar{x}+\sigma]=[90;110]\$

Taking logarithm of this gives \$[\log_{10}{90};\log_{10}{110}]=[1.95;2.04]=[2-0.05;2+0.04]\$



Back to your values:

\$\bar{x}=0.01807\$ and \$\sigma=0.0011435\$

Converting back to dBu with \$D(x)\$ being the inverse of the formula of point 1. of your question:

\$D(\bar{x})=85.139\$
\$D(\sigma)=61.165\$   &lt;- this is not he value you are searching for!

BUT:

\$D(\bar{x}-\sigma)=84.571\$
\$D(\bar{x}+\sigma)=85.672\$ 

So, the interval where 68% of all values reside, has a width of just 1.1.

You can't just convert \$\sigma\$ alone to dBu, you have to do it for \$\bar{x}\pm\sigma\$.



EDIT:

Here is a diagram showing what's going on. (Here, I used your exact values. Above values may differ due to rounding)



The violet curve shows your gauss-shaped noise distribution: Linear scale on the x-axis, log scale (dBu) on the y-axis.
The bright green and blue stripes indicate the 68% and 95% interval.
The red curve is \$D(x)\$.

In theory, you have to do the conversion for \$\bar{x}\pm 2.228\sigma\$ to get the upper / lower boundary of the 95% interval in dBu. However, the width of this interval is roughly about 2.228 times the width of the 68% interval, because the conversion function is almost linear in that range. As counterexample, have a look at the green curve!



Here is the data. The upper dataset is yours, the lower is for the green curve:

          |      Value      |    Diff to x     |
          | linear  | dBu   |  linear  |  dBu  |
..........|.........|.......|..........|.......|
x         | 0.01807 | 85.14 |          |       |
x+s       | 0.01951 | 85.80 |  0.00143 |  0.66 |
x-s       | 0.01664 | 84.42 |  0.00143 |  0.72 |
x+2.228s  | 0.02127 | 86.56 |  0.00320 |  1.41 |
x-2.228s  | 0.01488 | 83.45 |  0.00320 |  1.69 |
..........|.........|.......|..........|.......|
x         | 0.00500 | 73.98 |          |       |
x+s       | 0.00700 | 76.90 |  0.00200 |  2.92 |
x-s       | 0.00300 | 69.54 |  0.00200 |  4.44 |
x+2.228s  | 0.00946 | 79.51 |  0.00446 |  5.53 |
x-2.228s  | 0.00054 | 54.71 |  0.00446 | 19.27 |