Bullet Seating

[Montana Cowboy]

Howdy All
Need some suggestions as to what I'm doing wrong. When I seat a bullet in a .38 Special, .357 Magnum or .44 Magnum I just can't seem to do it without getting one side of the case to show a noticeable bulge at the base of the seated bullet while the other side is straight .
When I seat a bullet I do my best too start it straight / parallel as possible to the case. My seater die is just a bit loose to allow the ram and seating die with a case in the shell holder to align themselves with the press when the ram is run up to meet the seater die, then I lock it down. I then lightly touch the bullet with the seater plug to start the bullet into the case . As I seat the bullet I rotate the case a little thinking that if isn't started straight this would help align the bullet with the case.
Hope this makes sense, I'm watching my 2 yr old granddaughter today and this has taken me all day to write this. I love watching her but a 2 yr old requires your undivided attention. MC