I need a program that allows me to display the bootstraps without them overlapping with the branches. Figtree doesn't allow to move the data. Nor do the softwares allow me to edit from one to another software.
I'd export the tree into an SVG file from FigTree and then use vector graphics software (I have used Inkscape for that, you asked for the best software, Inscape is a bit tedious but it gets the job done) to edit labels manually.
Depending on the size of the tree, and the density and placement of the nodes, it may not be realistically feasible to display them all in such a way that no node labels overlap with branches.
Often, you'll see phylogenies displayed such that only node labels that are smaller than a certain threshold (e.g., bootstrap values less than 100) are actually displayed on the tree.
In any case, one alternative to manually editing with a vector graphics program (which may be your best option) is to check out ggtree, which has a lot of flexibility and options:
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version 2.3.6
Ultimately, the previous poster is correct that you will at some point end up importing your tree into a vector graphics program for final annotation. To amplify that point, most of the time you only want to have bootstrap values for a few major branches above a certain threshold. That number is almost always small enough that it's easiest to put those numbers in by hand in your drawing program.
That being said, Archaeopteryx has a great deal of functionality for editing trees, and there is some latitude for how bootstrap numbers are displayed.
To get an idea of what you can do with Archaeopteryx, see the tutorial Visualization of Phylogenetic Trees.