They chased down Ryde’s 125-3 with an over to spare to tee up a west region semi-final tie against Exeter University at Taunton on Sunday March 3.
Michael Porter (29), Phil Morris (29), Sam Kennett (25) and Brad Currie (23) were all unbeaten for Bashley.
Earlier, an unbeaten half-century by Dave Pratt (50), supported by Stu Robertson (25) underpinned the Ryde total. Steve Wilson took 2-26.
If Bashley beat the Exeter students, they will face Cheltenham Civil Service or the winners of the Wiltshire group, which will be decided at the Pewsey Sports Centre on Sunday, when Biddlestone, South Wilts or Swindon Indians lock horns in a round-robin affair.
The Hampshire indoor finals are at the Ageas Bowl this Saturday evening, initially at 6.30pm when holders Burridge defend their county crown against Sparsholt.
Hook & Newnham Basics play Waterlooville in the second semi-final at 7.40pm, with the winners contesting the 8.50pm final.
The Hampshire winners go to Canterbury on March 3 to face Ifield.