Thank you for your question. To Introduce myself I am a sydney based Solicitor and will do my best to provide you with relevant information to assist you.
Your bridging visa is based on the original visa you had. If your original visa did not permit you to work you cannot work and if you do then you are in breach and you will be deported.
If you are on Bridging Visa A or C you cannot travel and if you leave you will not be permtted entry back into Australia
You can travel on Bridging Visa B but you have to come back in the set period.
Here is the link from the department.
You cannot change between bridging visas. I am sorry to say.
You cannot make changes to these conditions.
Your visa E means you did not have a substantive visa when you went onto the bridging Visa.
You can make an application to the department to allow you to work and travel but you have to convince them.
Here is some information for you about this.
You will need to make an application to the department. If your Solicitor is not a Migration expert you may need to change Solicitors.
If you tell me what state you are in I can provide you with the law society details and they can refer you.