A couple of CCE members have posted about commuting from Midlothian in another thread.
I suspect more would be willing to cycle in if there was a better route - or the current routes were better.
Unfortunately geo-politics means that cycle policy/provisions alter at arbitrary (invisible) lines on the ground. Lothian Regional Council (1975–1996) did a lot of good work to encourage cycling - not least the creation of much of the North Edinburgh Path Network.
Since then City of Edinburgh has been actively reluctant to pay for 'cross-border' cycle routes on the basis that not many people (by implication, who are Edinburgh residents/council tax payers) would use them.
Phrase "chicken and egg" never made much impact.
SEStran has some responsibility for cycling. Its Business Plan 2008/09-2010/11 states "There are four main strands of SEStran work in sustainable transport: ■ travel plans, ■ car sharing, ■ cycling, and ■ sustainable transport policy."
One of its "Input to Single Outcome Agreements" - No. 44 - says "Cycling key connections, Edinburgh - Improve cycling links to and from Edinburgh." But then No. 3. is "Royal Infirmary Link Road - Improving accessibility to the new Royal Infirmary on the south side of Edinburgh, especially by bus."
The Borders Railway had proposals for a parallel cycle route in places - particular though the planned Midlothian settlement of Shawfair, which seems to be permanently on hold for economic reasons.
Infrastructure is very "chicken and egg".