Your byte array must have some encoding. The encoding cannot be ASCII if you've got negative values. Once you figure that out, you can convert a set of bytes to a String using:

byte[] bytes = {...}
String str = new String(bytes, StandardCharsets.UTF_8); // for UTF-8 encoding

There are a bunch of encodings you can use, look at the supported encodings in the Oracle javadocs.

The object your method decompressGZIP() needs is a byte[].

So the basic, technical answer to the question you have asked is:

byte[] b = string.getBytes();
byte[] b = string.getBytes(Charset.forName("UTF-8"));
byte[] b = string.getBytes(StandardCharsets.UTF_8); // Java 7+ only

However the problem you appear to be wrestling with is that this doesn't display very well. Calling toString() will just give you the default Object.toString() which is the class name + memory address. In your result [B@38ee9f13, the [B means byte[] and 38ee9f13 is the memory address, separated by an @.

For display purposes you can use:

Arrays.toString(bytes);

But this will just display as a sequence of comma-separated integers, which may or may not be what you want.

To get a readable String back from a byte[], use:

String string = new String(byte[] bytes, Charset charset);

The reason the Charset version is favoured, is that all String objects in Java are stored internally as UTF-16. When converting to a byte[] you will get a different breakdown of bytes for the given glyphs of that String, depending upon the chosen charset.

You can't just take the returned string and construct a string from it... it's not a byte[] data type anymore, it's already a string; you need to parse it. For example :

String response = "[-47, 1, 16, 84, 2, 101, 110, 83, 111, 109, 101, 32, 78, 70, 67, 32, 68, 97, 116, 97]";      // response from the Python script

String[] byteValues = response.substring(1, response.length() - 1).split(",");
byte[] bytes = new byte[byteValues.length];

for (int i=0, len=bytes.length; i<len; i++) {
   bytes[i] = Byte.parseByte(byteValues[i].trim());     
}

String str = new String(bytes);

** EDIT **

You get an hint of your problem in your question, where you say "Whatever I seem to try I end up getting a byte array which looks as follows... [91, 45, ...", because 91 is the byte value for [, so [91, 45, ... is the byte array of the string "[-45, 1, 16, ..." string.

The method Arrays.toString() will return a String representation of the specified array; meaning that the returned value will not be a array anymore. For example :

byte[] b1 = new byte[] {97, 98, 99};

String s1 = Arrays.toString(b1);
String s2 = new String(b1);

System.out.println(s1);        // -> "[97, 98, 99]"
System.out.println(s2);        // -> "abc";

As you can see, s1 holds the string representation of the array b1, while s2 holds the string representation of the bytes contained in b1.

Now, in your problem, your server returns a string similar to s1, therefore to get the array representation back, you need the opposite constructor method. If s2.getBytes() is the opposite of new String(b1), you need to find the opposite of Arrays.toString(b1), thus the code I pasted in the first snippet of this answer.