As written, this exercise is ambiguous, since we don't know how many bits make one character, or even if this number is constant or not. (For e.g. Unicode text using the UTF-8 encoding, it's not — one character can take up between 1 to 4 bytes, or 8 to 32 bits.)
However, if we assume that one character = one byte = 8 bits, then the message has 2003 × 8 = 16024 bits. This amounts to 250 (= 16000 / 64) full 64-bit cipher blocks, and 24 bits (= 3 bytes) left over, for a total of 251 blocks (= 251 × 64 = 16064 bits) after padding.
(A perhaps simpler way to calculate this is to note that 64 bits = 8 bytes, and that 2000 is a multiple of 8. Thus, the message has 2000 / 8 = 250 full blocks and 3 extra bytes, giving a total of 2008 bytes after 5 padding bytes have been appended to round the length up to the next multiple of 8 bytes.)