This is twice in one night I've had to play the health-professional card.
Is it something in the air this week?
First off, you don't necessarily need an expensive strap, just a decently padded/wide one to take the edge off the constant pressure. http://www.guitarcenter.com/Bass-Spe...cks.gc?ipp=100
I have a Planet Waves bass strap that works nicely. It took a little trial-and-error adjusting to find the "sweet spot" for maximum comfort, but once I got it, it was just fine. (By the way, check out the "Clearance Sale" link. It's good for in-store and online for another day or so)
Secondly, what you're subjecting yourself to is classic "repetitive stress" and is exactly what I'd be "professionally-getting-on-your-case" about. I'll spare you the list of problems that could arise from that amount of constant pressure on your neck/shoulder junction AND the ways the body winds itself up compensating for that pain.
The prescription is a little common sense.
…that, and maybe more cowbell.
1. If you're practicing while sitting down, don't strap on your bass. If you must "strap on" while you practice, keep a stand nearby so you can put it down while you web-surf. This way, you can…
2. Give your shoulders and neck an occasional breather. You're no less dedicated to practicing if you give your body a break, especially since…
3. You're not going to be inclined to play, gigging or practicing, if you're in constant pain.
There may be some other tips I could give, but I don't know the nuts-and-bolts details of how you play. There are tons of factors involved;
How high up on your body do you keep your axe?
What kind of chair you sit on while playing/surfing?
What other forms of repetitive stress affects you on a daily basis?
Other medical issues?
The list goes on and on.
Anyway, beyond the "common-sense-stuff", there's a lot of friendly advice I'm more than willing to pass on. Please don't hesitate to ask, and that goes for everybody who reads this post.
Chronic pain sucks, but there are ways to avoid and/or deal with it.
-Malak the Mad