might be a bit tight for me

[Silver]

Hi.

My friend Carol and I meet once a week; she's going back to the US soon. But this week I can't make it; I have so many things to do. I need to teach from Thursday night to Sunday evening. And I have some other things to do, so I can't make it. I texted Carol telling her that I can't make it this week, I started like "This week might be a bit tight for me" (So I can't make it for our once-a-week gathering)

I wonder if the bold is natural.

 

[Jektor]

Yes, it's normal English.
It means that it will be difficult to find the time to do something - it will be difficult to "fit something into" the time available (here, a week). This can be turned around into: "This week is going to be a tight fit" - "This week is going to be a bit tight for me" = "I may not have time to do everything that I want to this week".
.

 

[You little ripper!]

It perfectly idiomatic. Another option might be, I’ve got a really tight schedule this week. Can we make it next week?

 

[Silver]

Thanks a lot, Jektor and Little Ripper!