Visa type for mainland China to do passport work in BD embassy, Beijing?

Hi, I'm currently working at Taipei, Taiwan and a bangladeshi passport holder. I would like to go to Beijing for one day in August.

After two weeks in July, I'm going back to Bangladesh for a short stay. If I apply for L type in Chinese Embassy Dhaka, can I travel Taipei - Beijing - Taipei with that one in August?

Thank you in advance for your kind reply.