How to ask for a personal day off/ not quit while going out of state for a test

Here is the situation -
I have gotten an e-mail for a written exam for apprentice lineman for city of Burank, CA on 6/23.
I want to become a lineman, it's the dream job I'm gunning for right now.

Here is the conflict - I was recently hired as a trainee and started driving on 6/12. As a trainee, I need to be on the road for 5 weeks straight and test out. So, I thought that I wouldn't be able to make it to the Burbank test and crossed it off my mind.

But my OTR trainer rage quit two days ago due to problems with his truck that never got fixed properly (multiple times). Since the company found me a new trainer (he is local, so I get to stay at hotel every night in Phoenix, AZ) and the trainer was taking this Friday & next Monday off, I got to come home for a 4 day break.

So far the company has been good, and I really enjoy OTR experience on the flatbed. I'm trying to figure out how to make it to the test on next Thursday AND be training with the trucking company. I need to earn and pay the bills while I take the test and wait for results.

The company told me to be back in Phoenix, AZ by Tuesday morning.
I asked my trainer if it would be possible to take a day off to travel to Burbank, and he shook his head saying that the company hates it when the drivers take a break longer than their home time.


So here's my set of questions:

1. How do I request the company that I would like to take just one day off next week without telling them that I am testing for a different job?
a. Is saying, "I have a personal matter to attend" good enough?

2. Do you think a trainee/I can ask to start next next week, instead of next Tuesday?

I'm assuming that as a trainee, I have no leverage at all.
Although my priority lies within becoming an apprentice lineman, I don't want to burn a bridge/ be indirect about this problem. I don't want to quit so early; I have just finished the orientation and I have so much to learn about trucking!

Thanks for the advice.

 

lol that's what I assumed.
I need more inputs though. I will heed everyone's advice over night and decide tomorrow morning

 

I just realized, I could ask my DM if I could come in on Friday morning, instead of Tuesday after testing on Thursday! I could say personal matters for the reason. Thanks as usual, Chinatown!

 

I guess that i'll keep the details to myself.
TMI is always on point