Sure! Here's an example Bash script that does what you described:

```bash
#!/bin/bash

# Download the text file from the given URL
wget -qO- "https://example.com/urls.txt" | \
# Remove all lines beginning with a #
grep -v "^#" | \
# Download each URL and append to a single file
while read url; do
    wget -qO- "$url"
done >> output.txt
```

Here's a brief explanation of each line:

1. `#!/bin/bash`: This is called a shebang line, and it specifies the interpreter that should be used to run the script. In this case, we're using Bash.
2. `wget -qO- "https://example.com/urls.txt"`: This command downloads the text file from the given URL and prints it to standard output.
3. `grep -v "^#"`: This command filters out all lines beginning with a `#`.
4. `while read url; do ... done`: This loop reads each non-comment line from the input and assigns it to the variable `url`.
5. `wget -qO- "$url"`: This command downloads each URL specified in the text file and prints its contents to standard output.
6. `>> output.txt`: This appends the output of each downloaded file to the `output.txt` file.

Note that this script assumes that the URLs in the text file are one per line.
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