If the waterproof element (bottle etc.) you use has weight, you shouldn't need to add any more.  Otherwise I can suggest two ways to avoid overbalance.
1  Place stone or stones in the container.
2  Create a deeper base and include something heavy enough (stone, metal etc)

If you are developing a surface over glass, it is useful to cover it first with masking tape.  This creates a bond between the glass and paper.
After that you can laminate paper and/or pulp for a thicker texture.
To create deeper contours, you can use pulp or use a dry filling.  Yes, screwed up tape would work but I would recommend kitchen foil, pressed (even hammered) into shape and taped in position.

Thanks to both of you for the suggestions.  Borrowing from each of your posts, I think I will;
- first use a balloon of comparable diameter/circumference of the vitamin bottle as mould to create a globe shaped vase,
- cut out a hole in the dried globe to accommodate inserting the bottle
- place some pebbles or glass beads in the bottle to add weight (they will also provide an anchor for flower stem
- add additional layers of PM to close the opening and incorporate/disguise the bottle

On the inspiration piece, the artist seems to have used little, round, possibly rubber pads on the bottom to give the stability.  All in all, I figure that I'll experiment and I am still open to suggestions.   Thanx!

In looking at the vitamin bottle that I'll use for this project, which is about 4.5" in height and 2.5" in width, I realized that the vase could be sculpted as a solid piece with a hollow well. 

Paper pulp could be built up in whatever shape (globular, contoured etc.) I choose to give mass and then refined in subsequent layers.  The mass is both relatively small i.e. the globe would be 5" around, so it wouldn't take a a great amount of material and at the same time that material would add to the piece's weight (I'd still put in some pebbles in the bottle for the stability of a flower's stem and additional weight) 

The downside would be in drying time but that's more a matter of patience.

Any thoughts on this idea???

Koko,

I'm in the DC area, and my studio is in my basement so I have dehumidifiers running in all but winter. 

When I'm drying a piece I place it near the dehumidifier and with a small fan(s?) pointing at it.  I've been able to dry pieces with about 1/2" layer of paper mache clay in a few days.  When the piece is 'dry', but still cold to the touch, it isn't really dry.  Once the piece reaches room temperature, it seems to be safe to work with.   

I actually intentionally used 'thicker than I thought wise' amounts of clay on a project this spring just to see if I could get it to dry. 

-- b

Masks were the original interest ... and still important to me. 

Over the last 2 years I've done a series of pumpkins and gargoyles / etc. for Halloween display.  But honestly the interest order was paper mache and then Halloween, vs. being a true Halloween fanatic.  (In fact, I'm having a very hard time getting started this year, and time is definitely running out.)

I also create kazoo-based paper mache instruments called Kazoobas.  I had a 20-person marching band in the local 4th of July parade this year.  That was very fun.   And I played one last night at a ukulele recital I was a part of.

I've made a duplicate of my torso that functions as a dress form for altering shirts, etc.  and tried to make shoe lasts of a sort for my feet.  (The foot ones are definitely harder to do.)  And I have a taped 'thighs to neck' double of me that I just need to mache to make a real dress form for myself. 

I have an interest in paper mache furniture embellishment too ... but haven't moved on that yet.  (I'm getting progressively bigger in my experiments).

So my interest is pretty wide.  : )  The Kazoobas are probably the most original and personal thing I've done.  But I find I dive really deeply into something ... then need to walk away for a bit.

You?

-- b