Combine a 50/50 mixture of baking soda and water in a bowl and mix until it becomes a thick paste. You will need enough of the paste to completely cover the rust, so keep the bowl, baking soda, and water nearby in case you need to make more.  Baking soda is generally best at minor rust removal. Severe rusting may respond better to other methods.  Add a squirt of lemon juice to the paste for strengthened removal properties. Dab the paste on a brush or sponge and apply it to the rusty bike. Do not scrub or remove the paste immediately: it will need time to set and break down the rust. Let the paste sit for about 10 to 15 minutes. The baking soda paste should be thick enough to evenly coat the rust patch without dripping off of the bike. Using a plastic scrubber or steel wool, scrub the baking soda solution. As you scrub, you should notice the rust breaking down and detaching from the bike. If you do not notice this, add more of the baking soda paste to the bike and scrub with more force. Use a toothbrush as an alternative if no scrub pads are available. After you are finished scrubbing, leave the baking soda on for about 10-15 minutes to reach stubborn rust. Then, wipe off the paste with a dry microfiber cloth. Make sure the bicycle is completely dry to prevent further rusting.  Store the bike in a cool, dry place to keep the rust from returning. If there is still some rust left over, repeat the same process again or try another method.

Summary:
Mix baking soda and water in a bowl. Put the paste directly on the rust for about 15 minutes. Scrub the baking soda with a scrub pad. Wait about 10 minutes before wiping off the baking soda.