I'm applying to graduate school as a senior in my undergraduate studies. I know there's a good chance I won't get in, so I was hoping to ask the professor I am working under if I can research under him for a year while I apply again. What's the best way to ask if I can work under him as a backup option without sounding rude, and at what point should I ask?
For professor mentoring an undergraduate student, the broad goals for their students should be:
- Teach you about research - both how to do it and what it's like
- Get you to your next position, which is almost certainly someplace else
If you don't get into graduate school in your first run of applications, then these goals are still ongoing, and it's natural for you to stay. Of course there may be obstacles to this if you are graduating (sometimes positions can only be available to current students), but there's absolutely nothing to be cagey or secretive about. Graduate students are usually expected to go study somewhere besides where they were as an undergraduate. It's very natural both to a) have a backup plan and b) for your primary plan to be something besides being an undergraduate researcher for the rest of your life.
Whenever your next opportunity arises for a conversation, I'd simply ask your professor directly: "If I'm not successful in applying to graduate school this year, is it possible I could continue working for pay here in your lab?" is entirely appropriate. It's good to have this conversation early to help in planning finances. Your advisor should be hoping that your graduate applications are successful, but if they are able to support you they are likely to appreciate having an experienced worker continue.
I'm writing from the perspective of someone in the biomedical sciences in the US, where there is typically a fair amount of funding and flexibility available to support both undergraduate students and recent graduates in lab positions. In other fields these opportunities may not be available, but you probably can have a fairly good idea by looking around you at who the other people are.
A sit down conversation would be good, where you talk about your long term goals and mention that you might be delayed in starting grad school. Just ask if there are things they can help you with in terms of some project in the interim.
I don't think anyone would consider that rude.
And it is a good plan to keep connected, both to the field and to professors.
A sit down is far better than email since you have a chance for back and forth explorations.