The 3-5 day UPS rates might be close; not sure on the 1-2 day delivery. I have shipped many basses through eBay from Dallas, TX to the east and west coasts and it usually costs me around $60.00-$70.00.
However, these costs also include
Shipping box: $12-$15.00
Packing service: $10.00
Insurance: Depends on value
Request for signed delivery receipt: around $2.00
So, if you doubled the freight (southern CA to New Orleans) than the 3-5 days looks right (assuming it includes the above adders).
I have a good relationship with the local UPS shipping office (independent owners), so I use them for most of my shipments. However, I think that FedEx would be cheaper compared to UPS. I will never ship a bass USPS.
P.S. I have a couple of customers make their own arrangements with Federal Express. Thus, I simply print out the label and drop it off at the local FedEx office. I would recommend you do that.
P.P.S. I have been very fortunate that all of my shipments have been received without damage. Although it costs more, I always have the UPS office do the packing because if there is shipment damage, your claim should go through quickly. The problem most people have with the UPS claims is that they do their own packing and thus, the UPS claims office has to determine if it was packed correctly.