What you are looking for is to lock the formula.
The dollar sign
$ is used for "locking" a cell.
Form Responses 1'!$B$3 The cell is fully locked.
Form Responses 1'!$B3 The column of the cell is locked.
Form Responses 1'!B$3 The row of the cell is locked.
Form Responses 1'!B3 The cell is unlocked.
EDIT: (following OP comment)
What I need is =('Form Responses 1'!B$3) =('Form Responses 1'!C$3) on the next row down in the same column. Unless there is a better way to
Unlocked cells change the column letter when changing columns and row numbers when changing rows.
The easiest way to achieve what you want is manually:
1. Double click within the cell of the formula
='Form Responses 1'!B$3, highlight the whole of the formula and copy the text.
2. Go to the cell you want, double click within the cell and paste the text you have just copied and manually change the column letter from