Swiss Railways (SBB/CFF/FFS) operates a train from Basel to Rust hourly. Tickets cost $24 - $45 and the journey takes 41 min. FlixBus also services this route 3 times a day. Alternatively, BVB operates a bus from Basel to Rust every 15 minutes. Tickets cost $3 - $5 and the journey takes 12 min. Ouibus also services this route 6 times a week.
From Basel SBB train to Freiburg then line 007 bus to Rust. 2 h 16 min SFr 42. From Basel, Brausebad line 50 bus to Bâle Mulhouse Fribourg - Aéroport then bus to Europa Park. 3 h 22 min SFr 9. From Basel drive to Rust. 55 min SFr 14.