There was plenty of charm but no victory for the Bucks, who missed a hatful of chances.
Alastair Taylor eventually fired the hosts in front on 64 minutes but Ramsbottom levelled just minutes later with only their second real chance from Lee Gaskell.
The visitors fought off a constant siege of chances and were extremely lucky to come away with a point.
Former Morecambe man Joe McGee started for Bucks in his first appearance since joining earlier in the day.
Buxton flew out of the blocks and could have easily put the game to bed before half-time.
The hosts’ first chance came moments into the game when Taylor’s trickery and cross found the head of Bradley Barraclough unmarked but his header spun wide
Moments later, Ramsbottom charged on the counter and Lee Gaskell’s pace and turn inside caused problems for the hosts but his effort was well held by Jameson.
Barraclough was in again up the other end but his strike should have done more than sting Shenton’s gloves from 12 yards out.
Ramsbottom struggled to clear their lines in the early Buxton dominance and were lucky not to fall behind again.
Taylor’s half-volley pinballed around the box but no one could get the vital touch.
It was hands in the air again for Bucks boss Martin McIntosh as he bemoaned another missed chance as Liam Hardy fired over.
Jamie Green, Shuan Tuton and debutant McGee all added to Buxton’s shot tally but none troubled Shenton between the sticks before the break.
Taylor again was causing Lee Neville all sorts of problems down the right hand side and his run found Tuton who twisted and turned in the six-yard box but heroics from Matty Burke spurned the ball off the line.
The Bucks picked up where they left off and a fumble over the bar from Shenton nearly let Barraclough’s header cross the line.
Shenton made amends for his gaffe just minutes later when Tuton’s cross found the diving head of McGee but the Ramsbottom stopper saved well down low.
The visitors were counting their lucky stars as to how this game was still level after Tuton’s ball trickled across six-yard box but Greg Young spooned over just yards from goal.
Finally after long list of spurned chances, Bucks took the lead on 64 minutes.
Barraclough jinked inside to find Tuton centre of goal but instead of pulling the trigger he laid it on a plate for Taylor who slammed it home.
Buxton then switched off at the back as minutes later, against the run of play, Ramsbottom drew level.
A high ball into the box was headed down by the towering frame of Vinny Mukendi and Gaskell pounced on the edge with a volley that left Jameson rooted to the spot. Frustration began to grow as Bucks pressed for the winner - Ludlam headed over from an acute angle to add to the home sides finishing woes.
The visitors had to thank their captain again as he parried away a cross from Taylor that caused havoc in the box.
Shenton was then the hero as he pulled off an unbelievable block from Ash Palmer’s stinging strike right at the final whistle to deny Bucks a deserved winner.
Bucks: Jameson, Ludlam, Green, Niven, Palmer, Young, Taylor, McGee, Tuton, Hardy, Barraclough