I've re-finished a few bows and I've sent them off to be re-finished as well. Only you can decide if it will be worth the time and effort or expense of sending it off for refinishing.
Here are a couple of things to consider:
1) Is the bow in good, serviceable condition as is? Is it shootable and safe to use as is? Perhaps it is not very pretty but is it serviceable?
2) A lot of sanding may reduce the draw weight of the bow. Is this acceptable?
3) Keep in mind that removing all the decals from a vintage Bear Recurve reduces the bow's value considerably.
4) If this is a Bear recurve with GREEN GLASS, this fiber glass is very grainy, brittle, and splintery. Be careful. Difficult to work with. There are going to be striations in the green glass which may not come out at all. The black glass is much denser and much easier to work with. I simply don't care to work with the green fiberglass. Others might...
Here is how I re-finish a bow:
PREP WORK:
Write down the bow's specs on a piece of paper somewhere - serial #, AMO info, etc.
Wear leather or cotton gloves.
1) Remove the old finish with a Medium Grit sand paper or sanding sponges. Don't use too course a grit becaues it can cause the fiberglass to splinter. AVOID using a chemical stripper on the bow as it may permeate between the laminations, degrade the epoxy bond, and cause your limbs to start de-laminating.
2) Sand the entire bow with a fine grit sand paper. Focus on sanding out the deep dings and scratchess.
3) Sand entire bow with a very fine grit sand paper.
4) Repeat with an extra fine grit sand paper.
5) Repeat and continue stepping down until you are at @ 900 or even 1200 grit. Especially the fiber glass. We want to make sure we get ALL the chips, splinters, cracks, or blemishes out of the glass.
6) Obtain after market replacement decals if desired and available. But don't put them on the bow until after the first two or three coats of finish.
7) Clean entire bow well with denatured alcohol and let dry well.
8) Write the bow's spec info back on the bow. Wear cotton glove liners. Avoid finger prints and oil from your hands and fingers.
FINISHING
I have used several different spray finishes in aerosol cans. Some with very good results and some with very disappointing results... My favorite is the Min Wax Poly Clear in the Blue can. Its expensive - @ 9 bucks a can and you will need at least 2 cans but it is flexible enough when dry to be used on a bow. The Semi Gloss is fine. Shake the can frequently thoughout finishing and between coats.
The same stuff in a pint or quart can used in a professional air compressor spray gun is good stuff too. Perhaps you know someone with a wood shop or paint shop who will let you use his paint room and/or equipment or might simply spray the thing for you...
1) I hang the bow from one limb tip using floss or fishing line in a loop around the string grooves.
2) Spray very light, multiple coats of finish. Don't worry about missing spots. You'll get them on the next pass. When I say multiple coats, I mean 10 or 15 very light coats. This is not a quick process. Don't hold the can too close to the bow while spraying. You want each of the coats to be more of an "overspray" than a "direct spray". This will prevent runs and build ups.
3) Use long, even strokes up and down the length of the bow. Let the finish dry somewhat between coats.
4) When you have used the first can, let the finish dry and harden for at least 3 days before starting the second can.
5) On day 4, GENTLY wipe the bow down with 000 steel wool. Wear cotton glove liners or hold the bow with a cotton handkerchief to do this so you avoid getting oil and prints from your hands and fingers on the bow. Make sure you don't leave steel wool splinters on the bow. Wipe down with clean cotton cloth (maybe a cloth diaper)to remove steel wool shavings.
6) Repeat steps 1 through 4.
7) On Day 8, repeat step 5 using 0000 steel wool this time and you are done.
Anyway, that's how I have done it in the past. Works for me.
If there are any re-finishing gurus out there with more knowledge and experience and better techniques in mind, please speak up. I am a self taught re-finisher and I don't mind (and do appreciate) getting tips and guidance from those who know more about it than I do.