Modify Transformerless Power Supplies
Here is an online calculator for TPS in various configurations.

Play with the values and you will see that for 250mA load you will need a non polarised capacitor with a value over 4.7uf at 400V. At a quick search the capacitor I found is 25/25/35mm in volume and costs 3$. 

The TPS will have a low efficiency and your project very hard to debug. 

Please follow Wesley's and Indraneel's  advice and use a phone USB charger or something similar, some simple chargers can be tricked to output 3,3V It will be not only cheaper but also smaller , safer and will heat less.