I need to know how do I get to Mauville city without having a bike to get..

You don't need a bike to get there. Follow the grassy path leading east, the one next to the Trick Master's house. Follow it until you reach Mauville City.

NOTE: As you turn north on the path make sure your pok�mon are in top condition because you'll have a battle with May.

You can't use that cave,since you don't have the HM RockSmash which is in Mauvllie City,you have to go around by doing the task that Mr.Stone asked you too and finish it then you gain acces to the route to mauvllie

Mauville city........after beating saving slatport from the attack of the aqua at the Musuem..go back to rucborough and collect your reward..EXP.Share then go to the mauville city by walking in under the bike bridge thing, you will find your rival there and he/she will fight you and if you win you get an ItemFinder, just go all the way up and your there at Mauvllie City.

Try geodude and teach him Rock Smash...

Take the grassy path from Slateport to Mauville. You'll have to face your rival before you reach the city. There in Mauville you can get a Bike and HM06 (Rock Smash).

You don't need a bike to get there. If I'm right, that cave is right next to Defword town? If I'm correct, find Steven in that cave. You'll hand over the letter, gives you Steel wing, and left. If you're finished, go to the old guy (With his Pokemon Wingull) and he'll take you to Slateport city. You still have many things to do 'cause if I will type it all, it will take 2 years to finish. Hope I helped.

Go right under the bike path up to were you see may if you are on Pokemon emerold,ruby, or sappire

Just clear out the museum in slate port then try

Just before the Trick House go underneath and through the bridge with the Bikers. For the longest time I thought it was blocked off like a wall but there exists space underneath.