To determine the number of bond pairs (b.p.) and lone pairs (l.p.) in ${\mathrm{NO}}_3^{-}$, we first need to draw its Lewis structure.

Step 1: Calculate the total number of valence electrons.
Nitrogen (N) is in Group 15, so it has 5 valence electrons.
Oxygen (O) is in Group 16, so it has 6 valence electrons.
The ion has a -1 charge, so we add 1 electron.
Total valence electrons = $5+(3\times 6)+1=5+18+1=24$ electrons.

Step 2: Draw the skeletal structure.
Nitrogen is less electronegative than oxygen, so it will be the central atom. The three oxygen atoms are bonded to the central nitrogen atom.

Step 3: Distribute electrons to satisfy octets.
First, place 2 electrons (one single bond) between the central N atom and each O atom. This uses $3\times 2=6$ electrons.
Remaining electrons = $24-6=18$ electrons.
Distribute the remaining 18 electrons as lone pairs to the terminal oxygen atoms to complete their octets. Each oxygen needs 6 more electrons (3 lone pairs). This uses $3\times 6=18$ electrons.
Now, all oxygen atoms have an octet (2 bonding electrons + 6 lone pair electrons = 8 electrons). The central nitrogen atom has only 6 electrons (3 single bonds). To complete the octet of nitrogen, one of the lone pairs from an oxygen atom must be converted into a double bond between that oxygen and nitrogen.

Step 4: Determine bond pairs and lone pairs.
The Lewis structure of ${\mathrm{NO}}_3^{-}$ shows one N=O double bond and two N-O single bonds. Due to resonance, the double bond character is delocalized over all three N-O bonds, but for counting bond pairs, we consider the bonds formed.
Number of bond pairs (b.p.) = 1 (N=O) + 2 (N-O) = 4 bond pairs.
Number of lone pairs (l.p.) on the central nitrogen atom = 0. (The nitrogen atom has 4 bonds, satisfying its octet with no lone pairs).

Option Analysis:
A) $3$ b.p. $+1$ l.p.: Incorrect. The central nitrogen has 4 bonds and 0 lone pairs.
B) $4$ b.p. $+0$ l.p.: Correct. There are 4 bonds around the central nitrogen and no lone pairs on the central nitrogen.
C) $2$ b.p. $+2$ l.p.: Incorrect.
D) $1$ b.p. $+1$ l.p.: Incorrect.

Correct Answer: (B)