Here's how to go from the beginning of the game to Bowser in less than 30 minutes.
Step 1: Complete world 1 as usual. The yellow Switch is NOT needed for this.
Step 2: In the first level of world 2, grab a Cape Feather by jumping on a 'Super Koopa' with a flashy cape. Now, fly towards the end of the level and take the secret passage above-left of the finish.
Step 3: Next is a simple water level. The secret exit should be fairly easy to find. After this, enter the ghost house. Make sure you do NOT lose your cape. In the second room, take the P-Switch located on the left side of the room to the top-right. On the right side of this platform, activate the P-Switch and enter the blue door. Now, you will have to face Big Boo.
Step 4: Now it's time for Star Road. Here, you MUST find all the secret exits to progress. In the first level, break through blocks. As long as you stay on the right side, you should be able to find the exit. Next is another simple water level. Use the baby Yoshi to quickly swim to the top of the level until you reach a wall with a pipe. Do NOT enter the pipe, but go underneath it. Here is the secret exit. The following level should also be quite simple. Use the gray P-Switch to fly vertically. At the top, you will find the exit. The next level is the hardest level of this run, but as long as you stay flying at the bottom, you'll be fine. This level requires some practice if you want to play it perfectly. Now, take the star warp and you will end up in World Bowser.
Step 5: Now it's time for the final level. First, take door 2 and then door 5. After this, you will reach the final section. Once that's done, it's time for the final battle against Bowser.
Step 6: Congratulations! You have completed Super Mario World in a relatively short time!