A couple of notes first: when you use Data/data1.txt as an argument, should it really be /Data/data1.txt (with a leading slash)? Also, should the outer loop scan only for .txt files, or all files in /Data? Here's an answer, assuming /Data/data1.txt and .txt files only:
#!/bin/bash
for filename in /Data/*.txt; do
    for ((i=0; i<=3; i++)); do
        ./MyProgram.exe "$filename" "Logs/$(basename "$filename" .txt)_Log$i.txt"
    done
done
Notes:
- /Data/*.txtexpands to the paths of the text files in /Data (including the /Data/ part)
- $( ... )runs a shell command and inserts its output at that point in the command line
- basename somepath .txtoutputs the base part of somepath, with .txt removed from the end (e.g.- /Data/file.txt->- file)
If you needed to run MyProgram with Data/file.txt instead of /Data/file.txt, use "${filename#/}" to remove the leading slash. On the other hand, if it's really Data not /Data you want to scan, just use for filename in Data/*.txt.