Bodde struck in the 53rd minute as the Welsh side finally broke down a resolute Walsall side.
That was largely down to the heroics of Saddlers goalkeeper Clayton Ince, who somehow kept out Andy Robinson and Jason Scotland before Bodde's strike won it.
The Swans could even afford a late penalty miss from Darren Pratley as Ince kept out his late effort but their march to promotion continued.
Swansea made three changes from the side which drew at Crewe last weekend, with Alan Tate, Marcos Painter and Pratley all returning.
Walsall boss Richard Money was without experienced injured pair Darren Wrack and Tommy Mooney.
It was the Saddlers who began the better of the two sides, with Troy Deeney and Kevin Betsey having early chances for the in-form visitors.
Swansea then began to turn the screw and Ince somehow stuck out a foot to divert Ferrie Bodde's swerving long-range shot to safety in the 37th minute.
Ince was grateful to clutch Scotland's close range effort before Bodde fired just wide as Swansea became ever closer to breaking the deadlock.
Deeney forced De Vries into action moments after the break, but it was Swansea who took the lead when Bodde struck home his seventh of the season with a stunning long-range finish.
The Dutchman made room for himself before flashing a shot beyond Ince to open the scoring.
Andy Robinson then forced Ince into a great diving save before Swansea wasted a golden chance to extend their lead in the 79th minute when Ince kept out Pratley's weak penalty after Thomas Butler was tripped by Paul Boertien.
That let-off prompted the visitors to throw men forward in search of a leveller, with Deeney and substitute Ishmel Demontagnac going close to salvaging a late point.