That's always been my nemesis heading out in your direction. When I was doing some survey work for Sustrans, and bike bus stuff in Loanhead the cycling time matched that for catching the bus, so if there was no 37 or 62 in sight on Newington Road (to race to the next stop & jump aboard) then it took no longer to ride all the way (& walk up Liberton Brae)
I really think there is a campaign here to fill the generally 'empty' buses running later in the day (10-20 passengers on 80 passenger buses) and align with common formal or informal practice on several routes similar to Edinburgh-Penicuik with bikes allowed on board. Especially popular for example are late buses Hamilton-Strathaven where hill, headwind & unlit B road are strong disincentives to cycling.
I wonder if ScotGov commitment to Active Travel would stretch to delivering a trial of this on some bus services radiating from Edinburgh - West Coast Motors (ue Borders Buses) already does this officially on routes in Argyll & the West. 62 & 95 as the key routes, and perhaps ex-Perryman routes Edinburgh-Berwick (253) and Berwick-Melrose (67) with the old Munros Edinburgh-Jedburgh (51) as a further option
Perhaps just start with the 62 and possibly just part/parts of the route Edinburgh-Penicuik / Peebles-Galashiels Thoughts?