Remove substring from front and back of variable

I don't think that's possible (but would love to be proved wrong). However, you can use an intermediate variable. The bash -c run by -exec is just a bash instance, like any other:

$ find . -type f
./foobarbaz
$ find . -type f -exec bash -c 'v=${0#./foo}; echo ${v%baz}'  {} \;
bar

So I see no reason why this wouldn't work (if I understood what you're trying to do correctly):

find ./Source -name '*.src' \
     -exec bash -c 'v=${0%.src}; \ 
        myconvert -i "{}" -o "./Dest/${v#./Source/}.dst"' {} \;

The usual way is to do it in two steps:

x=foobarbaz
y=${x#foo}       # barbaz
z=${y%baz}       # bar

As this are "Parameter Expansions", a "Parameter" (variable) is needed to be able to perform any substitution. That means that y and z are needed. Even if they could be the same variable:

x=foobarbaz
x=${x#foo}       # barbaz
x=${x%baz}       # bar

---

find ./Source/ -name '*.src' -exec \
    bash -c '
        x=${1#./Source/}
        myconvert -i "$1" -o "./Dest/${x%.src}.dst"
    ' shname {} \;

Where shname is parameter $0 and the next {} is parameter $1 to the bash call.

---

A simpler alternative is to do a cd ./Source at the begining to avoid removing that part later. Something like:

cd ./Source                 ### Maybe test that it exist before cd to it.
shopt -s extglob nullglob   ### Make sure that correct options are set.

for f in *.src **/*.src; do
    echo \
    myconvert -i "$f" -o "./Dest/${f%.src}.dst"
done

Once you are convinced that it does what you want, comment out the echo.