Ira,
There is probably a little more to this than just putting the bike in a bag. Even in a travel bag a regular bike is going to be much larger than a folder so the size may still be an issue. And packing a bike in a travel bag requires quite a bit of breakdown - wheels off, pedals off, bar turned to side and down. It doesn't take all that long to break things down and put back together, but certainly more than I would want to deal with 4 times per day.
Depending on your situation and the length of the ride from the train stop to your workplace you might consider what a couple of other train commuters have reported doing. Get a beater bike, like an old 10 speed if you prefer a road bike or a mtb to leave locked up at the train stop near your workplace. Sure it's a risk, but that's why you use a $10-20 beater from Salvation Army or other thrift shop. If you only have a fairly short ride it doesn't even matter if it fits that well.
__________________
If it ain't broke, mess with it anyway!